# Past Seminars

Fri Dec 06

## MCFAM Seminar

5:30pm - Vincent Hall 16
GUN VIOLENCE: ACTUARIAL ANALYSIS AND MATHEMATICAL MODELING
Kristen Moore, University of Michigan
##### Abstract:

Firearm deaths and injuries are a significant problem in the United States. Indeed, the American Medical Association recently called firearm violence a public health crisis and called for a comprehensive public health response and solution. Gun violence in America exacts a significant toll on our society in both human and economic terms. Some argue that Americans have a moral obligation to address the issue of gun violence. But even from a more concrete perspective, the economic cost of firearms directly impacts the financial outcomes of insurers and taxpayers. There is a clear need for unbiased and objective research on the societal and economic impact of firearms. Actuaries are well positioned to study the mortality and morbidity related to firearms, both to quantify the risk and to inform governmental and public health interventions to mitigate the risk associated with firearms. Yet there is little on the topic in the actuarial and insurance literature. In this talk, I will provide a brief overview on the scope of firearm deaths and injuries and examine the extent to which actuaries and insurance professionals have studied or addressed the issue. I will compare firearm risk to risks that are considered in the underwriting process for life and homeowners insurance. I will describe some existing insurance products related to firearm risk as well as proposed legislation regarding gun liability insurance. In a different vein, if time permits, I will discuss preliminary work on a dynamical systems model of gun violence within a population. We are studying how, in an idealized model, changes to various policy parameters affect the long-term behavior of a system. Finally, I will describe some of the many open questions related to gun violence that are amenable to study by actuaries and mathematicians. Bio: https://sites.lsa.umich.edu/ksmoore/

Fri Dec 06

## Lie Theory Seminar

3:35pm - Vincent Hall 1
Special modular forms on exceptional groups
Aaron Pollack, Duke University
##### Abstract:

Classically, a Siegel modular form is said to be singular or distinguished if many of its Fourier coefficients are 0, in a precise sense. I will explain the construction of singular and distinguished modular forms on the exceptional groups E_6, E_7, E_8. Moreover, time permitting, I will also explain an analogue of the Saito-Kurokawa lift, which produces cusp forms on Spin(8) and the exceptional group G_2 out of holomorphic Siegel modular forms on Sp(4).

Fri Dec 06

## Combinatorics Seminar

3:30pm - Vincent Hall 570
A non-iterative formula for straightening fillings of Young diagrams
Reuven Hodges, UIUC
##### Abstract:

Young diagrams are fundamental combinatorial objects in representation theory and algebraic geometry. Many constructions that rely on these objects depend on variations of a straightening process that expresses a filling of a Young diagram as a sum of semistandard tableaux subject to certain relations. It has been a long-standing open problem to give a non-iterative formula for this straightening process. In this talk I will give such a formula. I will then use this non-iterative formula give a proof that the coefficient of the leading term in the straightening is either 1 or -1, generalizing a theorem of Gonciulea and Lakshmibai.

Fri Dec 06

## Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri Dec 06

## Math Biology Seminar

2:30pm - VinH 209
Math Biology Seminar

Fri Dec 06

## Probability Seminar

2:30pm - Vincent Hall 311
Gibbsian line ensembles and log-gamma polymers
Xuan Wu, Columbia University
##### Abstract:

In this talk we will first give an overview of the known
Gibbsian line ensembles in the KPZ universality class. Then we will
construct the discrete log-gamma line ensemble, which is associated
with the log-gamma polymers. This log-gamma line ensemble enjoys a
random walk Gibbs resampling invariance that follows from the
integrable nature of the log-gamma gamma polymer model via the
geometric RSK correspondence. By exploiting such resampling
invariance, we show the tightness of this log-gamma line ensemble
under the weak noise scaling. Furthermore, a Gibbs property, as
enjoyed by the KPZ line ensemble, holds for all subsequential limits.

Fri Dec 06

## Reading Seminar on Automorphic Forms

1:30pm - Vincent Hall 1
Reading Seminar on Automorphic Forms

Fri Dec 06

## Special Events and Seminars

1:25pm - Vincent Hall 213
"p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions
TBA
Fri Dec 06

## IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Lecture
Whitney Moore, University of Minnesota, Twin Cities
Fri Dec 06

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Probabilistic Preference Learning with the Mallows Rank Model for Incomplete Data
Arnoldo Frigessi, Oslo University Hospital
##### Abstract:

Personalized recommendations are useful to assist users in their choices in web-based market places, entertainment engines, information providers. Learning individual preferences is an important step. Users express their preferences by rating, ranking, (possibly inconsistently) comparing, liking and clicking items. Such data contain information about the individual users ranking of the items. Click-through data can be seen as (consistent) pair comparisons. The Mallows rank model allows to analyse rank data, but its computational complexity has limited its use to a particular form, based on Kendalls distance. We developed new computationally tractable methods for Bayesian inference in Mallows models that work with any right-invariant distance. Our method performs inference on the latent consensus ranking of all items and on the individual latent rankings by Bayesian augmentation. Current popular recommendation algorithms are based on matrix factorisations, have high accuracy and achieve good clickthrough rates. However diversity of the recommended items is often poor and most algorithms do not produce interpretable uncertainty quantifications of the recommendations. With a simulation study and real life data examples, we demonstrate that compared to matrix factorisation approaches, our Bayesian Mallows method makes personalized recommendations mpared to matrix factorisation approaches, our Bayesian Mallows method makes personalized recommendations.

Arnoldo Frigessi is professor of statistics at the University of Oslo, leads the Oslo Center for Biostatistics and Epidemiology and is director of BigInsight. BigInsight is a centre of excellence for research-based innovation, a consortium of industry, business, public actors and academia, developing model based machine learning methodologies for big data. Originally from Italy, where he had positions in Rome and Venice, he moved to Norway in 2019 as a researcher at the Norwegian Computing Centre, before he became professor at the University of Oslo.

Frigessi has developed statistical methodology motivated by specific problems in science, technology and industry. He has designed stochastic models to study principles, dynamics and patterns of complex dependence. Inference is usually based on computationally intensive stochastic algorithms. Currently, he has research collaborations in genomics, personalised therapy in cancer, infectious disease models, eHealth research, personalised and viral marketing, s

Thu Dec 05

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Dec 05

## Colloquium

3:35pm - Vincent Hall 16
Modular forms on exceptional groups
Aaron Pollack, Duke
##### Abstract:

When G is a reductive (non-compact) Lie group, one can consider automorphic forms for G. These are functions on the locally symmetric space X_G associated to G that satisfy some sort of nice differential equation. When X_G has the structure of a complex manifold, the _modular forms_ for the group G are those automorphic forms that correspond to holomorphic functions on X_G. They possess close ties to arithmetic and algebraic geometry. For certain exceptional Lie groups G, the locally symmetric space X_G is not a complex manifold, yet nevertheless possesses a very special class of automorphic functions that behave similarly to the holomorphic modular forms above. Building upon work of Gan, Gross, Savin, and Wallach, I will define these modular forms and explain what is known about them.

Thu Dec 05

## Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
McCleary Philbin, University of Minnesota
Thu Dec 05

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Einstein's gravity and stability of black holes
Pei-Ken Hung, MIT
##### Abstract:

Though Einstein's fundamental theory of general relativity has already celebrated its one hundredth birthday, there are still many outstanding unsolved problems. The Kerr stability conjecture is one of the most important open problems, which posits that the Kerr metrics are stable solutions of the vacuum Einstein equation. Over the past decade, there have been huge advances towards this conjecture based on the study of wave equations in black hole spacetimes and structures in the Einstein equation. In this talk, I will discuss the recent progress in the stability problems with special focus on the wave gauge.

Wed Dec 04

## Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Dec 04

## PDE Seminar

3:35pm - Vincent Hall 570
Multi-scale analysis of Jordan curves
Benjamin Jaye, Clemson University
##### Abstract:

In this talk we will describe how one can detect regularity in Jordan curves through analysis of associated geometric square functions. We will particularly focus on the resolution to a conjecture of L. Carleson. Joint work with Xavier Tolsa and Michele Villa (https://arxiv.org/abs/1909.08581).

Wed Dec 04

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Dec 03

## Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Dec 03

## Colloquium

3:30pm - Vincent Hall 16
Mirror symmetry and canonical bases for quantum cluster algebras
Travis Mandel, Univ. of Edinburgh
##### Abstract:

Mirror symmetry is a phenomenon which relates the symplectic geometry of one space X to the algebraic geometry of another space Y. One consequence is that a canonical basis of regular functions on Y can be defined in terms of certain counts of holomorphic curves in X. I'll discuss the application of this to (quantum) cluster algebras --- certain combinatorially defined algebras whose definition was motivated by the appearance of canonical bases in representation theory and Teichmüller theory.

Tue Dec 03

## Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Dec 03

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Exploiting Group and Geometric Structures for Massive Data Analysis
Zhizhen (Jane) Zhao, University of Illinois at Urbana-Champaign
##### Abstract:

In this talk, I will introduce a new unsupervised learning framework for data points that lie on or close to a smooth manifold naturally equipped with a group action. In many applications, such as cryo-electron microscopy image analysis and shape analysis, the dataset of interest consists of images or shapes of potentially high spatial resolution, and admits a natural group action that plays the role of a nuisance or latent variable that needs to be quotient out before useful information is revealed. We define the pairwise group-invariant distance and the corresponding optimal alignment. We construct a graph from the dataset, where each vertex represents a data point and the edges connect points with small group-invariant distance. In addition, each edge is associated with the estimated optimal alignment group. Inspired by the vector diffusion maps proposed by Singer and Wu, we explore the cycle consistency of the group transformations under multiple irreducible representations to define new similarity measures for the data. Utilizing the representation theoretic mechanism, multiple associated vector bundles can be constructed over the orbit space, providing multiple views for learning the geometry of the underlying base manifold from noisy observations. I will introduce three approaches to systematically combine the information from different representations, and show that by exploring the redundancy created artificially across irreducible representations of the transformation group, we can get drastically improved nearest neighbor identification, when a large portion of the true edges are corrupted. I will also show the application in cryo-electron microscopy image analysis.

Tue Dec 03

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Dec 03

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
No Seminar
Mon Dec 02

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Towards personalized computer simulation of breast cancer treatment
&nbsp;Arnoldo&nbsp;Frigessi&nbsp;&nbsp;, &nbsp;University of Oslo&nbsp;&nbsp;
##### Abstract:

Current personalized cancer treatment is based on biomarkers which allow assigning each patient to a subtype of the disease, for which treatment has been established. Such stratifiedpatient treatments represent a first important step away from one-size-fits-all treatment.However, the accuracy of disease classification comes short in the granularity of thepersonalization: it assigns patients to one of a few classes, within which heterogeneity inresponse to therapy usually is still very large. In addition, the combinatorial explosivequantity of combinations of cancer drugs, doses and regimens, makes clinical testingimpossible. We propose a new strategy for personalised cancer therapy, based on producing acopy of the patients tumour in a computer, and to expose this synthetic copy to multiplepotential therapies. We show how mechanistic mathematical modelling, patient specificinference and simulation can be used to predict the effect of combination therapies in a breastcancer. The model accounts for complex interactions at the cellular and molecular level, andis able of bridging multiple spatial and temporal scales. The model is a combination ofordinary and partial differential equations, cellular automata and stochastic elements. Themodel is personalised by estimating multiple parameters from individual patient data,routinely acquired, including histopathology, imaging and molecular profiling. The resultsshow that mathematical models can be personalized to predict the effect of therapies in eachspecific patient. The approach is tested with data from five breast tumours collected in arecent neoadjuvant clinical phase II trial. The model predicted correctly the outcome after 12weeks treatment and showed by simulation how alternative treatment protocols would haveproduced different, and some times better, outcomes. This study is possibly the first onetowards personalized computer simulation of breast cancer treatment incorporating relevantbiologically-specific mechanisms and multi-type individual patient data in a mechanistic andmultiscale manner: a first step towards virtual treatment comparison.Xiaoran Lai, Oliver Geier, Thomas Fleischer, Øystein Garred, Elin Borgen, Simon Funke,Surendra Kumar, Marie Rognes, Therese Seierstad, Anne-Lise Børressen-Dale, VesselaKristensen, Olav Engebråten, Alvaro Köhn-Luque, and Arnoldo Frigessi, Tow

Mon Dec 02

## Student Number Theory Seminar

3:35pm - Vincent Hall 1
Student Number Theory Seminar
Henry Twiss
Mon Dec 02

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied and Computational Mathematics Seminar

Mon Dec 02

## Colloquium

3:35pm - Vincent Hall 570
Analysis and geometry of free boundaries: recent developments
Mariana Smit Vega Garcia, Western Washington University
##### Abstract:

In the applied sciences one is often confronted with free boundaries, which arise when the solution to a problem consists of a pair: a function u (often satisfying a partial differential equation (PDE)), and a set where this function has a specific behavior. Two central issues in the study of free boundary problems and related problems in calculus of variations and geometric measure theory are:(1) What is the optimal regularity of the solution u?
(2) How smooth is the free boundary (or how smooth is a certain set related to u)?

In this talk, I will overview recent developments in obstacle type problems and almost minimizers of Bernoulli-type functionals, illustrating techniques that can be used to tackle questions (1) and (2) in various settings.

The study of the classical obstacle problem - one of the most renowned free boundary problems - began in the 60s with the pioneering works of G. Stampacchia, H. Lewy and J. L. Lions. During the past five decades, it has led to beautiful and deep developments in the calculus of variations and geometric partial differential equations. Nowadays obstacle type problems continue to offer many challenges and their study is as active as ever.
While the classical obstacle problem arises from a minimization problem (as many other PDEs do), minimizing problems with noise lead to the notion of almost minimizers. Interestingly, though deeply connected to "standard" free boundary problems, almost minimizers do not satisfy a PDE as minimizers do, requiring additional tools from geometric measure theory to address (1) and (2).

Mon Dec 02

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Dec 02

## Topology Seminar

2:30pm - Ford Hall 110
Topology and Arithmetic Statistics
Weiyan Chen, University of Minnesota
##### Abstract:

Topology studies the shape of spaces. Arithmetic statistics studies the behavior of random algebraic objects such as integers and polynomials. I will talk about a circle of ideas connecting these two seemingly unrelated areas. To illuminate the connection, I will focus on three concrete examples: (1) the Burau representation of the braid groups, (2) analytic number theory for effective 0-cycles on a variety, and (3) cohomology of the space of multivariate irreducible polynomials. These projects are parts of a broader research program, with numerous contributions by topologists, algebraic geometers, and number theorists in the past decade, and lead to many future directions yet to be explored.
(PS. This will be a rehearsal of a job talk accessible to the general audience. Any comments or suggestions are appreciated.)

Mon Dec 02

## Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Nov 29

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Nov 29

## Combinatorics Seminar

3:30pm - Vincent Hall 570
Combinatorics Seminar
No Seminar
Fri Nov 29

## Math Biology Seminar

2:30pm - VinH 209
Math Biology Seminar

Fri Nov 29

## Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri Nov 29

## Reading Seminar on Automorphic Forms

1:30pm - Vincent Hall 1
Reading Seminar on Automorphic Forms

Fri Nov 29

## Special Events and Seminars

1:25pm - Vincent Hall 213
"p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions
TBA
Thu Nov 28

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Nov 28

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Nov 28

## Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
TBA
Thu Nov 28

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Nov 27

## Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Nov 27

## PDE Seminar

3:35pm - Vincent Hall 570
Quantitative Absolute Continuity of Harmonic Measure, and the Lp Dirichlet Problem
Steve Hofmann, University of Missouri
##### Abstract:

For a domain ? ? Rd, quantitative, scale-invariant absolute continuity (more precisely, the weak-A? property) of harmonic measure with respect to surface measure on ??, is equivalent to the solvability of the Dirichlet problem for Laplaces equation, with data in some Lp space on ??, with p < ?. Drawing an analogy to the famous Wiener criterion, which characterizes the domains in which the classical Dirichlet problem, with continuous boundary data, can be solved, it is of interest to find criteria for Lp solvability, thus allowing for singular boundary data. We shall review known results in this direction, in which (within the past 18 months) a rather complete picture has now emerged.

Wed Nov 27

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Nov 26

## Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Nov 26

## Colloquium

3:35pm - Vincent Hall 16
Schrodinger solutions on sparse and spread-out sets
Xiumin Du, University of Maryland
##### Abstract:

If we want the solution to the Schrodinger equation to converge to its initial data pointwise, what's the minimal regularity condition for the initial data should be? I will present recent progress on this classic question of Carleson. This pointwise convergence problem is closely related to other problems in PDE and geometric measure theory, including spherical average Fourier decay rates of fractal measures, Falconer's distance set conjecture, etc. All these problems essentially ask how to control Schrodinger solutions on sparse and spread-out sets, which can be partially answered by several recent results derived from induction on scales and Bourgain-Demeter's decoupling theorem.

Tue Nov 26

## Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Nov 26

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Information Flow and Security Aspects in 1-2-1 Networks
Martina Cardone, University of Minnesota, Twin Cities
##### Abstract:

In this talk, we will discuss 1-2-1 networks, which offer a simple yet informative model for mmWave networks. In such networks, it is assumed that two nodes can communicate only if they point beams at each other, otherwise the signal is received well below the thermal noise floor. The focus of the talk will be on single unicast 1-2-1 networks, where the communication from a source to a destination is assisted by a number of relays. In the first part of the presentation, we will characterize the maximum flow of information over such 1-2-1 networks. In particular, we will show that the Shannon capacity can be approximated by routing information along a polynomial (in the network size) number of paths between the source and the destination, and that the scheduling of the node beam orientations can be efficiently performed. In the second part of the presentation, we will analyze the security aspect of such 1-2-1 networks in the presence of an external eavesdropper who wiretaps a set of edges of her choice. In particular, we will derive secure capacity results, which highlight fundamental differences between the traditional secure network coding and security over 1-2-1 networks.

Martina Cardone is currently a tenure-track Assistant Professor within the Electrical and Computer Engineering department at the University of Minnesota. She received her B.Sc. and her M.Sc. in Telecommunications Engineering from Politecnico di Torino, Italy in 2009 and 2011, respectively. As part of a double degree program, she also received a M.Sc. degrees in Telecommunications Engineering from Télécom ParisTech, France in 2011. In 2015, she received her Ph.D. in Electronics and Communications from Télécom ParisTech (with work done at Eurecom in Sophia Antipolis, France), where she worked with Professor Raymond Knopp and Professor Daniela Tuninetti. From July 2015 to August 2017 she was a post-doctoral research fellow in the Electrical and Computer Engineering department at the University of California, Los Angeles, where she worked with Professor Christina Fragouli. From November 2017 to January 2018, she was a post-doctoral associate in the Electrical and Computer Engineering department at the University of Minnesota. She regularly serves on the Technical Program Committee of IEEE workshops and conferences. Her main research interests are in network information theory, wireless communications, network privacy and secrecy, network coding and distributed computing. She was the reci

Tue Nov 26

## Colloquium

1:25pm - Vincent Hall 570
K-stability and moduli spaces of Fano varieties
Yuchen Liu, Yale University
##### Abstract:

Fano varieties are positively curved algebraic varieties which form one of the three building blocks in the classification. Unlike the case of negatively curved varieties, moduli spaces of Fano varieties (even smooth ones) can fail to be Hausdorff. K-stability was originally invented as an algebro-geometric notion characterizing the existence of K\"ahler-Einstein metrics on Fano varieties. Recently, people have found strong evidence toward constructing compact Hausdorff moduli spaces of Fano varieties using K-stability. In this talk, I will discuss recent progress in this approach, including an algebraic proof of the existence of Fano K-moduli spaces, and describing these moduli spaces explicitly. This talk is partly based on joint works with H. Blum and C. Xu.

Tue Nov 26

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology

Tue Nov 26

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Nov 25

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Nov 25

## Student Number Theory Seminar

3:35pm - Vincent Hall 1
Crystalline cohomology and Katz's conjecture
Shengkai Mao
##### Abstract:

Crystalline cohomology is a type of Weil cohomology theory that fills in the gap at $p$ in the family of $l$-adic cohomologies. It's introduced by Alexander Grothendieck and developed by Pierre Berthelot. We will briefly discuss what is crystalline cohomology and why we need it. With the help of Frobenius action, we can define a semi-linear morphism on crystalline cohomology which provides a Newton polygon. We will state the Katz's conjecture (which is proved by Mazur and Ogus) (slogan: Newton polygon lies above Hodge polygon) and show some applications (if time permits).

Mon Nov 25

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied and Computational Mathematics Seminar

Mon Nov 25

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Nov 25

## Topology Seminar

2:30pm - Ford Hall 110
Topology Seminar
TBA
Mon Nov 25

## Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Mon Nov 25

## Differential Geometry and Symplectic Topology Seminar

10:10am - Vincent Hall 203A
Differential Signatures and Algebraic Curves
Michael Ruddy,, Max Planck Institute
##### Abstract:

For the action of a group on the plane, the group equivalence problem for curves can be stated as: given two curves, decide if they are related by an element of the group. The signature method, using differential invariants, to answer the local group equivalence problem for smooth curves and its application to image science has been extensively studied. For planar algebraic curves under subgroups of the general linear group, we show that this provides a method to associate a unique algebraic curve to each equivalence class, the algebraic curve's signature curve. However, computing the implicit equation of the signature curve is a challenging problem. In this talk we consider signatures of algebraic curves, show how to compute the degree without computing its defining polynomial explicitly, and present some results on the structure of signature curves for generic algebraic curves of fixed degree. Additionally we show that this leads to a method to solve the group equivalence problem for algebraic curves using numerical algebraic geometry.

Fri Nov 22

## MCFAM Seminar

5:30pm - Vincent Hall 16
The impact of negative interest rate policy and its effectiveness of stimulating economic growth
Perry Li, University of Minnesota

According to the Bloomberg Barclays Global Aggregate Index, there were $17 trillion (or 30%) bonds traded with negative yields within that popular fixed income benchmark, at the end of August 2019. Government bonds in Germany, Japan, and Switzerland all carry negative yields - meaning investors will lose money to hold them to maturity. How did we get here? Are those policies introduced by global central banks, after the 2008 financial crisis, effective (to spur inflation)? In this talk, I seek to use some case studies like reserve banking system, asset bubbles, and currency war to explore this topic.Bio: https://www.linkedin.com/in/liyuepeng/ Fri Nov 22 ## Combinatorics Seminar 3:30pm - Vincent Hall 570 A Pieri rule for key polynomials Danjoseph Quijada, USC ##### Abstract: The Pieri rule for the product of a Schur function and a single row Schur function is notable for having an elegant bijective proof that can be intuited by the rules concise diagrammatic interpretation, to wit, by appending cells to a Young diagram. Now, key polynomials generalize Schur polynomials to a basis of the full polynomial ring, in which they also refine the Schubert basis via a nice formula. In this talk, I will describe a Pieri rule for the product of a key polynomial and a single row key polynomial that can be analogously interpreted as appending cells to a key diagram, albeit potentially dropping some cells in between each cell addition. I will also outline the main points of the rules bijective proof, and in the process hopefully illustrate the utility of understanding the rule from a diagrammatic perspective. Joint work with Sami Assaf. Fri Nov 22 ## Special Events and Seminars 3:30pm - Vincent Hall 20 Mass Scale Image Analysis For Automated Plant Phenotyping and Classification via Machine Learning Riley O'Neill, University of St. Thomas ##### Abstract: The capacity to quantify crop architecture and morphology is foundational to the development of higher yielding cultivars via hybridization and genetic engineering. However, at the mass scale required by the science, manual plant phenotyping with physical instruments is arduous, time consuming, subjective, and a leading cause of undergraduate burnout in the UMN plant genetics department. While the process has been slightly improved with manual image analysis, such is almost as time consuming and remains subject to human error. Thereby, in efforts to further expedite phenotyping processes, circumvent human error, and provide more detailed analyses, we aim to completely automate plant phenotyping processes for the UMN plant genetics department and beyond. Working from over 15,000 soybean plants, weve advanced robust image processing platforms for measuring petiole and stem length, leaf area, leaf shape via signature curves, and branch angles via energy minimization in 2D, and begun preliminary work at 3D reconstructions from 2D data for 3D branch angles and further analyses. After data extraction and verification, we plan to implement clustering algorithms and machine learning to automatically group plant phenotypes as well as conduct principal component analysis to assemble an allometry space and identify the primary genes of influence. Fri Nov 22 ## AMAAZE 3:30pm - Vincent Hall 20 Mass Scale Image Analysis For Automated Plant Phenotyping and Classification via Machine Learning Riley O'Neill, University of St. Thomas ##### Abstract: The capacity to quantify crop architecture and morphology is foundational to the development of higher yielding cultivars via hybridization and genetic engineering. However, at the mass scale required by the science, manual plant phenotyping with physical instruments is arduous, time consuming, subjective, and a leading cause of undergraduate burnout in the UMN plant genetics department. While the process has been slightly improved with manual image analysis, such is almost as time consuming and remains subject to human error. Thereby, in efforts to further expedite phenotyping processes, circumvent human error, and provide more detailed analyses, we aim to completely automate plant phenotyping processes for the UMN plant genetics department and beyond. Working from over 15,000 soybean plants, weve advanced robust image processing platforms for measuring petiole and stem length, leaf area, leaf shape via signature curves, and branch angles via energy minimization in 2D, and begun preliminary work at 3D reconstructions from 2D data for 3D branch angles and further analyses. After data extraction and verification, we plan to implement clustering algorithms and machine learning to automatically group plant phenotypes as well as conduct principal component analysis to assemble an allometry space and identify the primary genes of influence. Fri Nov 22 ## Math Biology Seminar 2:30pm - VinH 209 Math Biology Seminar Fri Nov 22 ## Probability Seminar 2:30pm - Vincent Hall 311 Spherical spin glass models Eliran Subag, New York University ##### Abstract: How many critical points does a smooth random function on a high-dimensional space typically have at a given height? how are their distances distributed? what is the volume or geometry of the level sets? can we design efficient optimization algorithms for the random function? For the spherical spin glass models, those questions are closely related to the structure of the Gibbs measures, which have been extensively studied in physics since the 70s. I will start with an overview of the celebrated Parisi formula and ultrametricity property. I will then describe an alternative method to analyze the Gibbs measure using critical points, in the setting of the pure spherical models. Finally, I will explain how the latter can be extended to all spherical models, using another (soft) geometric approach, while at the same time making rigorous and generalizing the famous Thouless-Anderson-Palmer approach from physics. Fri Nov 22 ## Reading Seminar on Automorphic Forms 1:30pm - Vincent Hall 1 Reading Seminar on Automorphic Forms Fri Nov 22 ## Special Events and Seminars 1:25pm - Vincent Hall 213 "p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions TBA Fri Nov 22 ## IMA/MCIM Industrial Problems Seminar 1:25pm - Lind 305 Machine Learning Problems at Target Mauricio Flores, Target Corporation ##### Abstract: PhD and Master's students would likely benefit the most from this talk. There will be some discussion on opportunities at Target. The introduction of this talk will provide an overview of the AI sciences organization at Target and discuss summer internship opportunities. The remainder of the talk will overview the kinds of machine learning problems Target deals with, and dive into three such problems, in the fields of recommender systems and computer vision. Mauricio Flores received his PhD in Applied Mathematics from the University of Minnesota in 2018, under the supervision of Jeff Calder & Gilad Lerman. He is currently a Lead AI Scientist at Target, where he builds machine learning as well as computer vision models for visually compatible recommendations, and more recently, for damage detection in Targets distribution centers. Thu Nov 21 ## Student Combinatorics Seminar 4:40pm - Vincent Hall 570 Student Combinatorics and Algebra seminar Thu Nov 21 ## Colloquium 3:35pm - Vincent Hall 16 Colloquium Thu Nov 21 ## Commutative Algebra Seminar 2:30pm - Vincent Hall 209 Commutative Algebra Seminar Erika Ordog, Duke University Thu Nov 21 ## Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Geometry of degenerating Calabi-Yau manifolds Ruobing Zhang, Stony Brook ##### Abstract: This talk concerns a family of "collapsing" Ricci-flat Kähler manifolds, namely Calabi-Yau manifolds, converging to a lower dimensional limit, which develop singularities arising in various contexts such as metric Riemannian geometry, complex geometry and degenerating nonlinear equations. A primary aspect is to formulate how well behaved or badly behaved such spaces can be in terms of the recently developed regularity theory. Under the above framework, our next focus is on a longstanding fundamental problem which is to understand singularities of collapsing Ricci-flat metrics along an algebraically degenerating family. We will give accurate characterizations of such metrics and explain possible generalizations. Thu Nov 21 ## Topology Seminar 7:00am - Skybox LOWER (Legs + Butt) @ Skybox - Skybox ##### Abstract: https://www.fitmetrix.io/webportal/schedulemobile/f9719b20-4914-e911-a97...(Legs%20%2B%20Butt)&dateRangeFrom=2019-11-21T07%3A00%3A00&dateRangeTo=2019-11-21T07%3A55%3A00&locationid=5854&classID=31918145 Wed Nov 20 ## Student Number Theory Seminar 3:35pm - Vincent Hall 6 Student Number Theory Seminar Wed Nov 20 ## PDE Seminar 3:35pm - Vincent Hall 570 Effective Poisson equation of density functional theory at positive temperature Li Chen, MIT ##### Abstract: Density functional theory (DFT) has been a very successful effective theory of many-body quantum mechanics. In particular, the Kohn-Sham (KS) equations of DFT serve as an accurate model for the electron densities. The KS equations are a case of the Schrodinger-Poisson equations whose electron-electron effective interaction potential only depends on the density of electrons. When the number of electrons are limited, the KS equation can be solved quickly by numerical method at temperature T = 0. Since physically interesting settings are at T > 0, we study the KS equations at positive temperature and give an iterative scheme to construct solutions. One important class of electronic structures described by the KS equations is a crystalline lattice. At positive temperature, we show that a local perturbation to a crystalline structure induces an electric field governed by the Poisson equation. The latter equation emerges as an effective equation of the KS equations. This is a joint work with Israel M. Sigal. Wed Nov 20 ## Automorphic Forms and Number Theory 3:35pm - Vincent Hall 213 Automorphic Forms and Number Theory Tue Nov 19 ## Special Events and Seminars 4:30pm - Vincent Hall 301 Arithmetic Geometry Seminar Tue Nov 19 ## Colloquium 3:30pm - Vincent Hall 16 Colloquium Tue Nov 19 ## Dynamical Systems 2:30pm - Vincent Hall 209 Dynamical Systems Seminar Tue Nov 19 ## Colloquium 2:30pm - Vincent Hall 16 Random matrix theory and supersymmetry techniques Tatyana Shcherbyna, Princeton University ##### Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a spacial structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY) . SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. Tue Nov 19 ## IMA Data Science Lab Seminar 1:25pm - Lind 305 Robust Representation for Graph Data Dongmian Zou, University of Minnesota, Twin Cities ##### Abstract: Modern data are usually high-dimensional with noise and corruption. A useful representation of data has to be robust and address the data structure. In this talk, I will first present a class of robust models called the scattering transform that can be used to generated features from graph data. In graph scattering transforms, the representation is generated in an unsupervised manner based on graph wavelets. It is approximately invariant to permutations and stable to signal or graph manipulations. Numerical results show that it works effectively for classification and community detection problems. Next, I will address how the structure of data can be found using autoencoders. Indeed, in the framework of autoencoders, graph scattering transform can be applied to the important task of graph generation. It shows state-of-the-art performance in link prediction and can be used to generate molecular samples. Tue Nov 19 ## Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Differential Geometry and Sympletic Topology TBA Tue Nov 19 ## Climate Seminar 11:15am - Vincent Hall 570 Climate Seminar TBA Tue Nov 19 ## Topology Seminar 10:30am - Skybox CORE @ Skybox - Skybox ##### Abstract: https://www.fitmetrix.io/webportal/schedulemobile/f9719b20-4914-e911-a97... Mon Nov 18 ## Student Number Theory Seminar 3:35pm - Vincent Hall 1 The Casselman-Shalika Formula for GL_2 Emily Tibor ##### Abstract: This talk will focus on the Casselman-Shalika formula for GL_2 over a non-Archimedean local field, which is an explicit formula for the values of the spherical Whittaker function. A good amount of time will be dedicated to explaining the necessary background including Whittaker models and spherical vectors, which come together to form the spherical Whittaker function. We will then be ready to discuss the formula, Casselman's method of calculating it, and its significance. Mon Nov 18 ## Applied and Computational Mathematics Seminar 3:35pm - Vincent Hall 6 Scalable Algorithms for Data-driven Inverse and Learning Problems Tan Bui-Thanh, UT-Austin ##### Abstract: Inverse problems and uncertainty quantification (UQ) are pervasive in scientific discovery and decision-making for complex, natural, engineered, and societal systems. They are perhaps the most popular mathematical approaches for enabling predictive scientific simulations that integrate observational/experimental data, simulations and/or models. Unfortunately, inverse/UQ problems for practical complex systems possess these the simultaneous challenges: the large-scale forward problem challenge, the high dimensional parameter space challenge, and the big data challenge. To address the first challenge, we have developed parallel high-order (hybridized) discontinuous Galerkin methods to discretize complex forward PDEs. To address the second challenge, we have developed various approaches from model reduction to advanced Markov chain Monte Carlo methods to effectively explore high dimensional parameter spaces to compute posterior statistics. To address the last challenge, we have developed a randomized misfit approach that uncovers the interplay between the Johnson-Lindenstrauss and the Morozov's discrepancy principle to significantly reduce the dimension of the data without compromising the quality of the inverse solutions. In this talk we selectively present scalable and rigorous approaches to tackle these challenges for PDE-governed Bayesian inverse problems. Various numerical results for simple to complex PDEs will be presented to verify our algorithms and theoretical findings. If time permits, we will present our recent work on scientific machine learning for inverse and learning problems. Mon Nov 18 ## Applied and Computational Math Colloquium 3:35pm - Vincent Hall 207 Applied and Computational Math Colloquium Mon Nov 18 ## Topology Seminar 3:30pm - Vincent Hall 301 Topology Seminar: TBA Mon Nov 18 ## Topology Seminar 2:30pm - Ford Hall 110 Topology Seminar TBA Mon Nov 18 ## Cockburn's Seminar 2:30pm - Ford Hall B15 Cockburn's Seminar Fri Nov 15 ## MCFAM Seminar 5:30pm - Vincent Hall 16 Data Science in the Life Insurance Industry Gary Hatfield, Securian/University of Minnesota ##### Abstract: Data Scientist has emerged as one of the hottest and most talked about jobs in the world today. In my talk, I will provide an overview of how data science has emerged in the insurance industry. I will give some examples of how data science is being applied in life insurance and describe how the Actuarial profession is adapting. Bio: https://mcfam.dl.umn.edu/people/gary-hatfield Fri Nov 15 ## Combinatorics Seminar 3:30pm - Vincent Hall 570 Simplicial generation of Chow rings of matroids Chris Eur, UC Berkeley ##### Abstract: Matroids are combinatorial objects that capture the essence of linear independence. We first give a gentle introduction to the recent breakthrough in matroid theory, the Hodge theory of matroids, developed by Adiprasito, Huh, and Katz. By combining two prominent recent approaches to matroids, tropical geometric and Lie/Coxeter theoretic, we give a new presentation for the Chow ring of a matroid that further tightens the interaction between combinatorics and geometry of matroids. We discuss various applications, including a simplified proof of the main portion of the Hodge theory of matroids. This is joint work with Spencer Backman and Connor Simpson. Fri Nov 15 ## Math Biology Seminar 2:30pm - Vincent Hall 311 Joint seminar in math biology and probability: Mathematical Modelling in Immunotherapy of Melanoma Anna Kraut, Bonn ##### Abstract: Mathematical models can support biomedical research through identification of key mechanisms, validation of experiments, and simulation of new therapeutic approaches. We investigate the evolution of melanomas under adoptive cell transfer therapy with cytotoxic T-cells. It was shown in experiments that phenotypic plasticity, more precisely an inflammation-induced, reversible dedifferentiation, is an important escape mechanism for the tumor. Recently, the effects of possible mutation to a permanently resistant genotype were studied by introducing knockout melanoma cells into the wildtype tumor. We use a stochastic individual-based Markov process to describe the evolution of the tumor under various therapeutic approaches. It is an extension of the model introduced in the paper of Baar et al in 2016 and further includes the effects of T-cell exhaustion and some limited spatial component which results in additional non-linearities. The model is implemented as a hybrid algorithm that combines Gillespie-type stochastic calculations and a deterministic approximation to speed up simulations while keeping the effects of random events. Numerical simulations confirm the resistance to therapy via phenotypic switching as well as genotypic mutation. T-cell exhaustion is identified as an important mechanism that is crucial in fitting the model to the experimental data. We gain further insights into how originally unfit knockout cells can accumulate under therapy, shield the wild type cells from the T-cells, and thus cause an earlier relapse. Going beyond the experiment, the possibility of naturally occurring rare mutations, in contrast to artificially introduced knockout cells, is explored in simulations and produces the same effects. Thus, the clinical relevance of the experimental findings can be confirmed. Fri Nov 15 ## Dynamical Systems 2:30pm - Vincent Hall 20 The mathematics of taffy pulling Jean-Luc Thiffeault, University of Wisconsin ##### Abstract: Taffy is a type of candy made by repeated 'pulling' (stretching andfolding) a mass of heated sugar. The purpose of pulling is to get air bubbles into the taffy, which gives it a nicer texture. Until the late 19th century, taffy was pulled by hand, an arduous task. The early 20th century saw an avalanche of new devices to mechanize the process. These devices have fascinating connections to the topological dynamics of surfaces, in particular with pseudo-Anosov maps. Special algebraic integers such as the Golden ratio and the lesser-known Silver ratio make an appearance, as well as more exotic numbers. We examine different designs from a mathematical perspective, and discuss their efficiency. This will be a "colloquium style" talk that should be accessible to graduate students. Fri Nov 15 ## Probability Seminar 2:30pm - Vincent Hall 311 Joint seminar in math biology and probability: Mathematical Modelling in Immunotherapy of Melanoma Anna Kraut, Bonn ##### Abstract: Mathematical models can support biomedical research through identification of key mechanisms, validation of experiments, and simulation of new therapeutic approaches. We investigate the evolution of melanomas under adoptive cell transfer therapy with cytotoxic T-cells. It was shown in experiments that phenotypic plasticity, more precisely an inflammation-induced, reversible dedifferentiation, is an important escape mechanism for the tumor. Recently, the effects of possible mutation to a permanently resistant genotype were studied by introducing knockout melanoma cells into the wildtype tumor. We use a stochastic individual-based Markov process to describe the evolution of the tumor under various therapeutic approaches. It is an extension of the model introduced in the paper of Baar et al in 2016 and further includes the effects of T-cell exhaustion and some limited spatial component which results in additional non-linearities. The model is implemented as a hybrid algorithm that combines Gillespie-type stochastic calculations and a deterministic approximation to speed up simulations while keeping the effects of random events. Numerical simulations confirm the resistance to therapy via phenotypic switching as well as genotypic mutation. T-cell exhaustion is identified as an important mechanism that is crucial in fitting the model to the experimental data. We gain further insights into how originally unfit knockout cells can accumulate under therapy, shield the wild type cells from the T-cells, and thus cause an earlier relapse. Going beyond the experiment, the possibility of naturally occurring rare mutations, in contrast to artificially introduced knockout cells, is explored in simulations and produces the same effects. Thus, the clinical relevance of the experimental findings can be confirmed. Fri Nov 15 ## Reading Seminar on Automorphic Forms 1:30pm - Vincent Hall 1 Reading Seminar on Automorphic Forms Fri Nov 15 ## Special Events and Seminars 1:25pm - Vincent Hall 213 "p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions TBA Fri Nov 15 ## IMA/MCIM Industrial Problems Seminar 1:25pm - Lind 305 Pipelines, Graphs, and the Language of Shopping: Architecting Next Gen Machine Learning Capabilities for Retail Jonah White, Best Buy ##### Abstract: This talk will highlight the evolution of building out a data science capability in a retail environment as well as explore cutting-edge developments in constructing machine learning pipelines in the cloud, emerging advancements in time-series forecasting, applications of GPU accelerated graph processing for entity resolution, and how were adapting the latest research in language models to translate the language of shopping for the ultimate personalized experience Thu Nov 14 ## Student Combinatorics Seminar 4:40pm - Vincent Hall 570 Student Combinatorics and Algebra seminar Thu Nov 14 ## Colloquium 3:35pm - Vincent Hall 16$p$-adic estimates for exponential sums on curves Joe Kramer-Miller, UC Irvine ##### Abstract: A central problem in number theory is that of finding rational or integer solutions to systems of polynomials in several variables. This leads one naturally to the slightly easier problems of finding solutions modulo a prime$p$. Using a discrete analogue of the Fourier transformation, this modulo$p$problem can be reformulated in terms of exponential sums. We will discuss$p$-adic properties of such exponential sums in the case of higher genus curves as well as connections to complex differential equations. Thu Nov 14 ## Commutative Algebra Seminar 2:30pm - Vincent Hall 209 Commutative Algebra Seminar Gennady Lyubeznik, University of Minnesota Thu Nov 14 ## Colloquium 2:30pm - Vincent Hall 16 Applications of Frobenius beyond prime characteristic. Daniel Hernández, Univ. of Kansas ##### Abstract: Abstract: Recall that the Frobenius morphism is simply the map sending an element in a ring of prime characteristic$p>0$-- say, a polynomial with coefficients in a finite field -- to its$p$-th power. Though simple to define, Frobenius has proven to be a useful and effective tool in algebraic geometry, representation theory, number theory, and commutative algebra. Furthermore, and remarkably, some of the most interesting applications of Frobenius are to the study of objects defined over the complex numbers, and more generally, over a field of characteristic zero! In this talk, we will discuss some of these applications, with an eye towards classical singularity theory and birational algebraic geometry, both over the complex numbers. Thu Nov 14 ## Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Differential Geometry and Sympletic Topology TBA Wed Nov 13 ## Student Number Theory Seminar 3:35pm - Vincent Hall 6 Student Number Theory Seminar Wed Nov 13 ## Automorphic Forms and Number Theory 3:35pm - Vincent Hall 213 Counting points and varieties and Malle's conjecture Andy Odesky, University of Michigan Wed Nov 13 ## PDE Seminar 3:30pm - Vincent Hall 570 Serrin Lecture - Localization for the Anderson-Bernoulli model on the integer lattice Charles Smart, University of Chicago ##### Abstract: I will give a brief mathematical introduction to Anderson localization followed by a discussion of my recent work with Jian ding. In our work we establish localization near the edge for the Anderson Bernoulli model on the two dimensional lattice. Our proof follows the program of Bourgain--Kenig and uses a new unique continuation result inspired by Buhovsky--Logunov--Malinnikova--Sodin. I will also discuss recent work of by Li and Zhang on the three dimensional case. Tue Nov 12 ## Special Events and Seminars 4:30pm - Vincent Hall 301 Arithmetic Geometry Seminar Tue Nov 12 ## Colloquium 3:30pm - Vincent Hall 16 Colloquium Tue Nov 12 ## Dynamical Systems 2:30pm - Vincent Hall 209 Dynamical Systems Seminar Tue Nov 12 ## Colloquium 2:30pm - Vincent Hall 16 Unraveling Local Cohomology Emily Witt, Univ. of Kansas ##### Abstract: Local cohomology modules are fundamental tools in commutative algebra, due to the algebraic and geometric information they carry. For instance, they can help determine the number of equations necessary to define an affine variety. Unfortunately, however, the application of local cohomology is limited by the fact that these modules are typically very large (e.g., not finitely generated), and can be difficult to determine explicitly. In this talk, we discuss new techniques developed to understand the structure of local cohomology (e.g., coming from invariant theory). We also describe recently-discovered "connectedness properties" of spectra that local cohomology encodes. Tue Nov 12 ## IMA Data Science Lab Seminar 1:25pm - Lind 305 Latent Factor Models for Large-scale Data Xiaoou Li, University of Minnesota, Twin Cities ##### Abstract: Latent factor models are widely used to measure unobserved latent traits in social and behavioral sciences, including psychology, education, and marketing. Motivated by the applications of latent factor models to large-scale measurements which consist of many manifest variables (e.g. test items) and a large sample size, we study the properties of latent factor models under an asymptotic setting where both the number of manifest variables and the sample size grows to infinity. In this talk, I will introduce generalized latent factor models under exploratory and confirmatory settings. For the exploratory setting, we propose a constrained joint maximum likelihood approach for model estimation and investigate its theoretical properties. For the confirmatory setting, we study how the design information affects the identifiability and estimability of the model, and propose a rate-optimal estimator when the model is identifiable. The estimators can be efficiently computed through parallel computing. Our results provide insights on the design of large-scale measurement and have important implications on measurement validity. Tue Nov 12 ## Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Differential Geometry and Sympletic Topology TBA Tue Nov 12 ## Climate Seminar 11:15am - Vincent Hall 570 Climate Seminar TBA Mon Nov 11 ## Applied and Computational Math Colloquium 3:35pm - Vincent Hall 207 Applied and Computational Math Colloquium Mon Nov 11 ## Student Number Theory Seminar 3:35pm - Vincent Hall 1 Introduction to Rankin-Selberg Method Shengmei An ##### Abstract: Rankin-Selberg method has been one of the most powerful techniques for studying the Langlands program. In this talk, we will start with the original simplest example of the Rankin-Selberg method, and then come to a more general case of the Rankin-Selberg method on GL_m*GL_n where we can reduce the global integral to the more accessible lovely local integrals so that we can establish some of the important analytic properties of the L-functions. Mon Nov 11 ## Applied and Computational Mathematics Seminar 3:35pm - Vincent Hall 6 Applied and Computational Mathematics Seminar Mon Nov 11 ## Topology Seminar 3:30pm - Vincent Hall 301 Topology Seminar: TBA Mon Nov 11 ## Topology Seminar 2:30pm - Ford Hall 110 Cochain models for the unit group of a differential graded algebra Tyler Lawson, University of Minnesota ##### Abstract: Abstract not available. Mon Nov 11 ## Cockburn's Seminar 2:30pm - Ford Hall B15 Cockburn's Seminar Fri Nov 08 ## MCFAM Seminar 5:30pm - Vincent Hall 16 MCFAM Seminar Fri Nov 08 ## Combinatorics Seminar 3:30pm - Vincent Hall 570 Combinatorics via Deligne Categories Chris Ryba, MIT ##### Abstract: The Deligne category Rep(S_t) can be thought of as "interpolating" the representation categories of symmetric groups. After describing this category, I will explain how a calculation in the Deligne category can be used to prove stability properties of permutation patterns within conjugacy classes (joint with Christian Gaetz). Fri Nov 08 ## Math Biology Seminar 2:30pm - Vincent Hall 311 Joint seminar in math biology and probability: Mathematical Modelling in Immunotherapy of Melanoma Anna Kraut, Bonn ##### Abstract: Mathematical models can support biomedical research through identification of key mechanisms, validation of experiments, and simulation of new therapeutic approaches. We investigate the evolution of melanomas under adoptive cell transfer therapy with cytotoxic T-cells. It was shown in experiments that phenotypic plasticity, more precisely an inflammation-induced, reversible dedifferentiation, is an important escape mechanism for the tumor. Recently, the effects of possible mutation to a permanently resistant genotype were studied by introducing knockout melanoma cells into the wildtype tumor. We use a stochastic individual-based Markov process to describe the evolution of the tumor under various therapeutic approaches. It is an extension of the model introduced in the paper of Baar et al in 2016 and further includes the effects of T-cell exhaustion and some limited spatial component which results in additional non-linearities. The model is implemented as a hybrid algorithm that combines Gillespie-type stochastic calculations and a deterministic approximation to speed up simulations while keeping the effects of random events. Numerical simulations confirm the resistance to therapy via phenotypic switching as well as genotypic mutation. T-cell exhaustion is identified as an important mechanism that is crucial in fitting the model to the experimental data. We gain further insights into how originally unfit knockout cells can accumulate under therapy, shield the wild type cells from the T-cells, and thus cause an earlier relapse. Going beyond the experiment, the possibility of naturally occurring rare mutations, in contrast to artificially introduced knockout cells, is explored in simulations and produces the same effects. Thus, the clinical relevance of the experimental findings can be confirmed. Fri Nov 08 ## Probability Seminar 2:30pm - Vincent Hall 311 "Robust Synchronization via Cycle Consistency Inference Yunpeng Shi, UMN ##### Abstract: We propose a strategy for improving the existing methods for solving synchronization problems that arise from various computer vision tasks. Specifically, our strategy identifies severely corrupted relative measurements based on cycle consistency information. To the best of our knowledge, this paper provides the first exact recovery guarantees using cycle consistency information. This result holds for a noiseless but corrupted setting as long as the ratio of corrupted cycles per edge is sufficiently small. It further guarantees linear convergence to the desired solution. We also establish stability of the proposed algorithm to sub-Gaussian noise. Fri Nov 08 ## Reading Seminar on Automorphic Forms 1:30pm - Vincent Hall 1 Reading Seminar on Automorphic Forms Fri Nov 08 ## Special Events and Seminars 1:25pm - Vincent Hall 213 "p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions Steven Sperber Thu Nov 07 ## Student Combinatorics Seminar 4:40pm - Vincent Hall 570 Student Combinatorics and Algebra seminar Thu Nov 07 ## Colloquium 3:35pm - Vincent Hall 16 Eisenstein Series on Loop Groups and their Metaplectic Covers Manish Patnaik, University of Alberta ##### Abstract: Both the Langlands-Shahidi method of studying automorphic L-functions and approach via the theory of Weyl group multiple Dirichlet series to studying moments of L-functions now require new classes of groups with which to work. In this talk, I will explain our progress on extending these techniques to certain infinite-dimensional Kac-Moody groups, namely loop groups (and their metaplectic covers). Of note in our work is the presence of two quite different types of Eisenstein series that exist on the same group and which need to be considered in conjunction with one other. This is a report on joint work in progress with H. Garland, S.D. Miller, and A. Puskas. Thu Nov 07 ## Commutative Algebra Seminar 2:30pm - Vincent Hall 209 The spectral sequence of a filtered complex Gennady Lyubeznik, University of Minnesota ##### Abstract: This is the third of a series of three talks on the spectral sequence of a filtered complex. This material is by now classical and is an important part of homological algebra. The main difficulty in dealing with spectral sequences is that there are a lot of indexes involved and this is a considerable obstacle to understanding what is going on. The goal of these talks is to present this material, including most proofs, in an accessible manner. Thu Nov 07 ## Colloquium 2:30pm - Vincent Hall 16 On various questions (and answers) in High-dimensional probability Galyna Livshyts, Georgia Tech ##### Abstract: In this talk, several topics from High-dimensional probability shall be discussed. This fascinating area is rich in beautiful problems, and several easy-to-state questions will be outlined. Further, some connections between them will be explained throughout the talk. I shall discuss several directions of my research. One direction is invertibility properties of inhomogeneous random matrices: I will present sharp estimates on the small ball behavior of the smallest singular value of a very general ensemble of random matrices, and will briefly explain the new tools I developed in order to obtain these estimates. Another direction is isoperimetric-type inequalities in high-dimensional probability. Such inequalities are intimately tied with concentration properties of probability measures. Among other results, I will present a refinement of the concavity properties of the standard gaussian measure in an n-dimensional euclidean space, under certain structural assumptions, such as symmetry. This result constitutes the best known to date estimate in the direction of the conjecture of Gardner and Zvavitch from 2007. The above topics will occupy most of the time of the presentation. In addition, I shall briefly mention other directions of my research, including noise-sensitivity estimates for convex sets, or, in other words, upper bounds on perimeters of convex sets with respect to various classes of probability distributions. If time permits, I will discuss my other results, such as small ball estimates for random vectors with independent coordinates, and partial progress towards Levi-Hadwiger illumination conjecture for convex sets in high dimensions. Thu Nov 07 ## Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Differential Geometry and Sympletic Topology TBA Wed Nov 06 ## Student Number Theory Seminar 3:35pm - Vincent Hall 6 Student Number Theory Seminar Wed Nov 06 ## PDE Seminar 3:35pm - Vincent Hall 570 PDE Seminar Wed Nov 06 ## Automorphic Forms and Number Theory 3:35pm - Vincent Hall 213 The automorphic heat kernel from a geometric perspective Amy DeCelles, St. Thomas Tue Nov 05 ## Special Events and Seminars 4:30pm - Vincent Hall 301 Arithmetic Geometry Seminar Tue Nov 05 ## Colloquium 3:30pm - Vincent Hall 16 Colloquium Tue Nov 05 ## Dynamical Systems 2:30pm - Vincent Hall 209 Dynamical Systems Seminar Tue Nov 05 ## IMA Data Science Lab Seminar 1:25pm - Lind 305 Topics in Sparse Recovery via Constrained Optimization: Least Sparsity, Solution Uniqueness, and Constrained Exact Recovery Seyedahmad Mousavi, University of Minnesota, Twin Cities ##### Abstract: Sparse recovery finds numerous applications in different areas, for example, engineering, computer science, business, applied mathematics, and statistics. Sparse recovery is often formulated as relatively large-scale and challenging constrained (convex or nonconvex) optimization problems. Constraints are ubiquitous and important in many applications of sparse recovery, but they make analysis and computation nontrivial and require novel techniques to handle them. The goal of this talk is to present numerical and analytical techniques for constrained sparse recovery using convex analysis and optimization tools. Three topics are investigated in the realm of constrained sparse recovery. First, we analyze quantitative adverse properties of different$p$-norm-based optimization problems with$p>1$, such as generalized basis pursuit, basis pursuit denoising, ridge regression, and elastic net. We show that their optimal solutions are least sparse for almost all measurement matrices and measurement vectors. Second, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. We apply these solution uniqueness results to a broad class of$\ell_1$-minimization problems in constrained sparse optimization, such as basis pursuit, LASSO, and polyhedral gauge recovery. Third, we propose a constrained matching pursuit algorithm for constrained sparse recovery and develop uniform conditions for exact support and vector recovery on constraint sets. The exact recovery via this algorithm not only depends on a measurement matrix but also critically relies on a constraint set. Hence, we identify an important class of constraint sets, called coordinate projection admissible. We then use the conic hull structure of these sets together with constrained optimization techniques to establish sufficient conditions for uniform exact recovery via this algorithm on coordinate projection admissible sets. These conditions are expressed in terms of the restricted isometry-like and the restricted orthogonality-like constants Tue Nov 05 ## Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Differential Geometry and Sympletic Topology TBA Tue Nov 05 ## Climate Seminar 11:15am - Vincent Hall 570 Climate Seminar TBA Mon Nov 04 ## Applied and Computational Math Colloquium 3:35pm - Vincent Hall 207 Applied and Computational Math Colloquium Mon Nov 04 ## Student Number Theory Seminar 3:35pm - Vincent Hall 1 Rankin-Selberg Method May Shengmei Mon Nov 04 ## Applied and Computational Mathematics Seminar 3:35pm - Vincent Hall 6 Applied differential geometry and harmonic analysis in deep learning regularization Wei Zhu, Duke University ##### Abstract: Deep neural networks (DNNs) have revolutionized machine learning by gradually replacing the traditional model-based algorithms with data-driven methods. While DNNs have proved very successful when large training sets are available, they typically have two shortcomings: First, when the training data are scarce, DNNs tend to suffer from overfitting. Second, the generalization ability of overparameterized DNNs still remains a mystery. In this talk, I will discuss two recent works to inject the modeling flavor back into deep learning to improve the generalization performance and interpretability of the DNN model. This is accomplished by DNN regularization through applied differential geometry and harmonic analysis. In the first part of the talk, I will explain how to improve the regularity of the DNN representation by enforcing a low-dimensionality constraint on the data-feature concatenation manifold. In the second part, I will discuss how to impose scale-equivariance in network representation by conducting joint convolutions across the space and the scaling group. The stability of the equivariant representation to nuisance input deformation is also proved under mild assumptions on the Fourier-Bessel norm of filter expansion coefficients. Mon Nov 04 ## Topology Seminar 3:30pm - Vincent Hall 301 Topology Seminar: TBA Mon Nov 04 ## Topology Seminar 2:30pm - Ford Hall 110 Topology Seminar TBA Mon Nov 04 ## Cockburn's Seminar 2:30pm - Ford Hall B15 Cockburn's Seminar Fri Nov 01 ## MCFAM Seminar 5:30pm - Vincent Hall 16 Extrapolative Expectations, Financial Frictions, and Asset Prices Yao Deng, University of Minnesota ##### Abstract: I study how extrapolative expectations affect corporate real and financial activities and asset prices. Empirically, high misperception on earnings growth, a measure constructed to proxy for extrapolation, is associated with an increase in investment, debt issuance, equity issuance, and firm-level bond and stock prices in the short-term, but predicts a decline in all these activities and prices in the long-term. These patterns are more pronounced among small and financially constrained firms. Theoretically, I build a dynamic model with extrapolative expectations and financial frictions, and show that the interaction of these two frictions is crucial to explain the empirical findings. Intuitively, after a sequence of favorable shocks, agents extrapolate and become overoptimistic about future productivities. Firms invest and borrow more in the short-term. Lower perceived default probability improves financing conditions, further increasing investment and borrowing. Future realizations turn out worse than expected, making real and financial activities and asset prices subject to predictable reversals in the long-term.Bio: https://carlsonschool.umn.edu/faculty/yao-deng Fri Nov 01 ## Combinatorics Seminar 3:30pm - Vincent Hall 570 Combinatorics Seminar Dongkwan Kim, UMN ##### Abstract: For a Coxeter group W, a W-graph is a graph which produces a nice basis of the corresponding representation of W and also describes the action of W on the basis elements. Even when W is finite and its irreducible characters are known, W-graphs are still useful for understanding representations of W. In this talk, I will talk about W-graphs when W is an (extended) affine symmetric group, especially when these graphs are associated with two-row partitions. Also I will discuss the connection between them and Lusztigs periodic W-graph. This work is joint with Pavlo Pylyavskyy. Fri Nov 01 ## Probability Seminar 2:30pm - Vincent Hall 311 Probability Seminar Fri Nov 01 ## Reading Seminar on Automorphic Forms 1:30pm - Vincent Hall 1 Reading Seminar on Automorphic Forms Fri Nov 01 ## Special Events and Seminars 1:25pm - Vincent Hall 213 p-Adic Banach Spaces and Completely Continuous Endomorphisms Steven Sperber Thu Oct 31 ## Student Combinatorics Seminar 4:40pm - Vincent Hall 570 Student Combinatorics and Algebra seminar Thu Oct 31 ## Colloquium 3:35pm - Vincent Hall 16 Differential operators on invariant rings Anurag Singh, University of Utah ##### Abstract: Work of Levasseur and Stafford describes the rings of differential operators on various classical invariant rings of characteristic zero; in each of these cases, the differential operators form a simple ring. Towards an attack on the simplicity of rings of differential operators on invariant rings of reductive groups over the complex numbers, Smith and Van den Bergh asked if reduction modulo p works for differential operators in this context. In joint work with Jack Jeffries, we establish that this is not the case for various classical groups. Thu Oct 31 ## Commutative Algebra Seminar 2:30pm - Vincent Hall 209 Spectral sequences Gennady Lyubeznik, University of Minnesota ##### Abstract: This is the first of a series of three talks on the spectral sequence of a filtered complex. This material is by now classical and is an important part of homological algebra. The main difficulty in dealing with spectral sequences is that there are a lot of indexes involved and this is a considerable obstacle to understanding what is going on. The goal of these talks is to present this material, including most proofs, in an accessible manner. Thu Oct 31 ## Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Differential Geometry and Sympletic Topology TBA Wed Oct 30 ## Student Number Theory Seminar 3:35pm - Vincent Hall 6 Student Number Theory Seminar Wed Oct 30 ## PDE Seminar 3:35pm - Vincent Hall 570 PDE Seminar Wed Oct 30 ## Automorphic Forms and Number Theory 3:35pm - Vincent Hall 213 Automorphic Forms and Number Theory Tue Oct 29 ## Special Events and Seminars 4:30pm - Vincent Hall 301 Arithmetic Geometry Seminar Tue Oct 29 ## Colloquium 3:30pm - Vincent Hall 16 Colloquium Tue Oct 29 ## Dynamical Systems 2:30pm - Vincent Hall 209 Dynamical Systems Seminar Tue Oct 29 ## IMA Data Science Lab Seminar 1:25pm - Lind 305 Highly Likely Clusterable Data With No Cluster Mimi Boutin, Purdue University ##### Abstract: Data generated as part of a real-life experiment is often quite organized. So much so that, in many cases, projecting the data onto a random line has a high probability of uncovering a clear division of the data into two well-separated groups. In other words, the data can be clustered with a high probability of success using a hyperplane whose normal vector direction is picked at random. We call such data highly likely clusterable. The clusters obtained in this fashion often do not seem compatible with a cluster structure in the original space. In fact, the data in the original space may not contain any cluster at all. This talk is about this surprising phenomenon. We will discuss empirical ways to detect it as well as how to exploit it to cluster datasets, especially datasets consisting of a small number of points in a high-dimensional space. We will also present a possible mathematical model that would explain this observed phenomenon. This is joint work with Alden Bradford (Purdue Math), Sangchun Han (Purdue ECE, now at Google) and Tarun Yellamraju (Purdue ECE, now at Qualcomm). Mireille (Mimi) Boutin graduated with a bachelors degree in Physics-Mathematics from the University of Montreal. She received the Ph.D. degree in Mathematics from the University of Minnesota under the direction of Peter J. Olver. She joined Purdue University after a post-doctorate with David Mumford, David Cooper, and Ben Kimia at Brown University, Rhode Island, followed by a post-doctorate with Stefan Muller at the Max Plank Institute for Mathematics in the Sciences in Leipzig, Germany. She is currently an Associate Professor in the School of Electrical and Computer Engineering, with a courtesy appointment in the Department of Mathematics. Her research is in the area of signal processing, machine learning, and applied mathematics. She is a three-time recipient of Purdues Seed for Success Award. She is also a recipient of the Eta Kappa Nu Outstanding Faculty Award, the Eta Kappa Nu Outstanding Teaching Award and the Wilfred Duke Hesselberth Award for Teaching Excellence. Tue Oct 29 ## Differential Geometry and Symplectic Topology Seminar 1:25pm - Vincent Hall 570 Differential Geometry and Sympletic Topology TBA Tue Oct 29 ## Climate Seminar 11:15am - Vincent Hall 570 Convergence and Equilibrium for Stochastic Models of Ecological Disturbances James Broda, Bowdoin College Mon Oct 28 ## Applied and Computational Math Colloquium 3:35pm - Vincent Hall 207 Applied and Computational Math Colloquium Mon Oct 28 ## Student Number Theory Seminar 3:35pm - Vincent Hall 1 "Part 2: Representation Stability, Étale Cohomology and Combinatorics of Configuration Spaces over Finite Fields" David DeMark ##### Abstract: After introducing the theory of FI-modules in 2012, the collaborative unit consisting of Thomas Church, Jordan Ellenberg and Benson Farb applied their framework to asymptotically stable counting problems in a certain classes of FI-varieties over finite fields in their 2013 paper Representation stability in cohomology and asymptotics for families of varieties over finite fields. The paper serves as a proof-of-concept, unifying a number of previously-known combinatorial results. The key to their method is the Grothendieck-Lefschetz fixed-point theorem with twisted statistics, which relates the rational cohomology of an algebraic variety over the complex numbers with the trace of the Frobenius map applied to the étale cohomology with coefficients in an$\ell$-adic sheaf of that variety over a finite field. In this talk, we shall introduce the Grothendieck-Lefschetz formula and its associated machinery as well as FI-modules and representation stability, then use these ideas to give an exposition of some results of Church, Ellenberg and Farb as they relate to configuration spaces and the braid group. Mon Oct 28 ## Applied and Computational Mathematics Seminar 3:35pm - Vincent Hall 6 Applied and Computational Mathematics Seminar Mon Oct 28 ## Topology Seminar 3:30pm - Vincent Hall 301 Topology Seminar: TBA Mon Oct 28 ## Topology Seminar 2:30pm - Ford Hall 110 Compactifying the étale topos Elden Elmanto, Harvard University ##### Abstract: The speaker has long feared the technicalities and intricacies of equivariant stable homotopy theory. Fortunately, beginning with the work of Glasman, major simplification on the foundations of the subject has been made (cf. the work of Ayala-Mazel-Gee-Rozenblyum, Nikolaus-Scholze and the Barwick school). We offer another perspective (that the speaker has a chance of understanding) on equivariant stable homotopy theory, at least for the group C_2, via algebraic geometry. We view it as a way to remedy an infamous annoyance: the 2-étale cohomological dimension of the field of real numbers is infinite. We do this by identifying the genuine C_2-spectra with a category of motives based on Real algebraic geometry ala Scheiderer. This is joint work with Jay Shah. Mon Oct 28 ## Cockburn's Seminar 2:30pm - Ford Hall B15 Cockburn's Seminar Fri Oct 25 ## MCFAM Seminar 5:30pm - Vincent Hall 16 Mortgage Prepayment Behavior Messan Edorh and Bo Li, US Bank ##### Abstract: According to the US Census Bureau, homeownership rates peaked during the first quarter of 2005 at 69.1% but fell to just 63.8% in the fourth quarter of 2015, a year when residential mortgage debt outstanding was still above ten trillion-dollar mark and mortgage origination was about$1.7T. Mortgage Back Security (MBS) originations have continued to experience a steady growth attracting investors, servicers, insurers, lenders, and GSEs (Government Sponsored Enterprises). In contrary, MBS market presented various financial risks including prepayment from the homeowners - be that voluntary or involuntary.

To manage the risks presented by the borrowers, modeling prepayment behavior is critical in the work banks do. Four fundamental components of mortgage prepayment activity will be examined in this presentation.

Fri Oct 25

## Combinatorics Seminar

3:30pm - Vincent Hall 570
Combinatorial Methods for Integrable Systems
Nick Ovenhouse.
##### Abstract:

An integrable Hamiltonian system is a dynamical system with "enough conserved quantities" to guarantee that it can, in principle, be solved, or "integrated". I will give some basic definitions of Poisson algebras and what it means to be integrable in this context. I will then show, by way of an example (namely the "pentagram map"), how some combinatorial techniques using weighted directed graphs can be used to model the system and demonstrate its integrability. This method also hints at connections with cluster algebras and Postnikov's constructions related to stratifications of the positive Grassmannian. Time permitting, I will also discuss recent work generalizing this example.

Fri Oct 25

## Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar
Kevin Leder, UMN
Fri Oct 25

## Reading Seminar on Automorphic Forms

1:30pm - Vincent Hall 1
Reading Seminar on Automorphic Forms

Fri Oct 25

## Special Events and Seminars

1:25pm - Vincent Hall 213
"p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions
TBA
Fri Oct 25

## IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Gamma Guidance - The Mathematics Applied to a Launch Vehicle
Gary Green, The Aerospace Corporation
##### Abstract:

The Boeing Inertial Upper Stage (IUS) launch vehicle was used to launch spacecraft from 1982 until 2004. The Gamma Guidance algorithm was used on board the IUS to select the ignition times, durations, and directions of engine firings. I will discuss the mathematics employed in Gamma Guidance as well as collateral on-board ;processes in order to illuminate how mathematics is applied in the launch setting.

Dr. Gary Green holds mathematics degrees from the Universities of Idaho, Michigan State, and Pennsylvania State. He taught mathematics at California State College Stanislaus before joining the Aerospace Corporation (www.aerospace.org), where he served as an applied mathematician and systems engineer in several capacities: employing numerical analysis to model launch vehicles, overseeing algorithm and software development for space systems, evaluating space system performance, and analyzing threats against space systems.

Thu Oct 24

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Oct 24

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Oct 24

## Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Spectral Sequences
Gennady Lyubeznik, University of Minnesota
##### Abstract:

This is the first of a series of three talks on the spectral sequence of a filtered complex.
This material is by now classical and is an important part of homological algebra.
The main difficulty in dealing with spectral sequences is that there are a lot of indexes involved and this is a considerable obstacle to understanding what is going on. The goal of these talks is to present this material, including most proofs, in an accessible manner.

Thu Oct 24

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Oct 23

## Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Oct 23

## PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Wed Oct 23

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Oct 22

## Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Oct 22

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Oct 22

## Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Oct 22

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Convergence Rates and Semiconvexity Estimates for the Continuum Limit of Nondominated Sorting
Brendan Cook, University of Minnesota, Twin Cities
##### Abstract:

Multiobjective optimization problems are ubiquitous in science and engineering contexts, and nondominated sorting is a sorting process fundamental to multiobjective optimization. Recently proposed approaches to nondominated sorting exploit an underlying PDE that arises in the continuum limit. The need for theoretical guarantees for nondominated sorting algorithms motivates the problem of finding rates of convergence for the continuum limit. In this talk I will introduce PDE techniques from the theory of viscosity solutions and show how they can be used to solve this problem. Furthermore, I will show how semiconvexity estimates can be used to bolster convergence rates, and discuss approaches to obtaining semiconvexity estimates. This talk is intended to be entirely self-contained, so no prior knowledge of PDE will be assumed.

Tue Oct 22

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Oct 22

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Oct 21

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Oct 21

## Student Number Theory Seminar

3:35pm - Vincent Hall 1
"Representation Stability, Étale Cohomology and Combinatorics of Configuration Spaces over Finite Fields"
David DeMark
##### Abstract:

After introducing the theory of FI-modules in 2012, the collaborative unit consisting of Thomas Church, Jordan Ellenberg and Benson Farb applied their framework to asymptotically stable counting problems in a certain classes of FI-varieties over finite fields in their 2013 paper Representation stability in cohomology and asymptotics for families of varieties over finite fields. The paper serves as a proof-of-concept, unifying a number of previously-known combinatorial results. The key to their method is the Grothendieck-Lefschetz fixed-point theorem with twisted statistics, which relates the rational cohomology of an algebraic variety over the complex numbers with the trace of the Frobenius map applied to the étale cohomology with coefficients in an $\ell$-adic sheaf of that variety over a finite field. In this talk, we shall introduce the Grothendieck-Lefschetz formula and its associated machinery as well as FI-modules and representation stability, then use these ideas to give an exposition of some results of Church, Ellenberg and Farb as they relate to configuration spaces and the braid group.

Mon Oct 21

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied and Computational Mathematics Seminar

Mon Oct 21

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Oct 21

## Topology Seminar

2:30pm - Ford Hall 110
Descent properties of topological Hochschild homology
Liam Keenan, University of Minnesota
##### Abstract:

Algebraic K-theory is an extremely rich but notoriously difficult invariant to compute. In order to make calculations tractible, topological Hochschild homology and topological cyclic homology were introduced, along with the Dennis and cyclotomic trace maps. A natural question to consider is whether or not these invariants are sheaves for various topologies arising in algebraic geometry. In fact, it turns out that topological Hochschild homology is a sheaf for the fpqc topology on connective commutative ring spectra. In this talk, I plan to introduce the language necessary and sketch the argument of this result.

Mon Oct 21

## Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Oct 18

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Oct 18

## Combinatorics Seminar

3:30pm - Vincent Hall 570
Combinatorics Seminar

Fri Oct 18

## Probability Seminar

2:30pm - Vincent Hall 311
Rare events in the spectrum of random matrices
Kevin Leder, UMN
##### Abstract:

In this talk I will consider extreme behavior of the extremal eigenvalues of white Wishart matrices, which play an important role in multivariate analysis. I will focus on the case when the dimension of the feature p is much larger than or comparable to the number of observations n, a common situation in modern data analysis. I will discuss asymptotic approximations for the tail probabilities of the extremal eigenvalues. In addition, I will discuss the construction of an efficient Monte Carlo importance sampling algorithm to estimate the tail probabilities. Simulation results show that our method has the best performance among known approximation approaches, and furthermore provides an efficient and accurate way for evaluating the tail probabilities in practice. Based on joint work with Tiefieng Jiang and Gongjun Xu.

Fri Oct 18

## Reading Seminar on Automorphic Forms

1:30pm - Vincent Hall 1
Reading Seminar on Automorphic Forms

Fri Oct 18

## Special Events and Seminars

1:25pm - Vincent Hall 213
Trace Formula, continued
Steven Sperber, University of Minnesota
Thu Oct 17

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Oct 17

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Oct 17

## Colloquium

3:35pm - Vincent Hall 16
Hopf monoids relative to a hyperplane arrangement
Marcelo Aguiar, Cornell University
##### Abstract:

The talk is based on recent and ongoing work with Swapneel
Mahajan. We will introduce a notion of Hopf monoid relative to a real
hyperplane arrangement. When the latter is the braid arrangement, the
notion is closely related to that of a Hopf monoid in Joyal's category
of species, and to the classical notion of connected graded Hopf
algebra. We are able to extend many concepts and results from the
classical theory of connected Hopf algebras to this level. The
extended theory connects to the representation theory of a certain
finite dimensional algebra, the Tits algebra of the arrangement. This
perspective on Hopf theory is novel even when applied to the classical
case. We will outline our approach to generalizations of the classical
Leray-Samelson, Borel-Hopf, and Cartier-Milnor-Moore theorems to this
setting. Background on hyperplane arrangements will be reviewed.

Thu Oct 17

## Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
Rebecca R.G., George Mason University
Thu Oct 17

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Oct 16

## Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Oct 16

## PDE Seminar

3:35pm - Vincent Hall 570
Optimal local well-posedness for the derivative nonlinear Schrodinger's equation
Yu Deng, University of Southern California
##### Abstract:

In joint work with Andrea Nahmod and Haitian Yue, we prove local well-posedness for the derivative nonlinear Schrodinger's equation in Fourier-Lebesgue space which has the same scaling as H^s for any s>0. This closes the gap left open by the work of Grunrock-Herr where s>1/4. Here there is no trilinear estimate in any standard function space, instead we will construct the solution in a nonlinear submanifold (of a function space) by exploiting its structure. This is somehow inspired by the theory of para-controlled distributions that Gubinelli et al. developed for stochastic PDEs, but our arguments are purely deterministic.

Wed Oct 16

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Oct 15

## Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Oct 15

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Oct 15

## Dynamical Systems

2:30pm - Vincent Hall 209
Forecasting U.S. elections with compartmental models of infection
Alexandria Volkening, Northwestern University
##### Abstract:

U.S. election forecasting involves polling likely voters, making assumptions about voter turnout, and accounting for various features such as state demographics and voting history. While political elections in the United States are decided at the state level, errors in forecasting are correlated between states. With the goal of shedding light on the forecasting process and exploring how states influence each other, we develop a framework for forecasting elections in the U.S. from the perspective of dynamical systems. Through a simple approach that borrows ideas from epidemiology, we show how to combine a compartmental model with public polling data from HuffPost and RealClearPolitics to forecast gubernatorial, senatorial, and presidential elections at the state level. Our results for the 2012 and 2016 U.S. races are largely in agreement with those of popular pollsters, and we use our new model to explore how subjective choices about uncertainty impact results. We conclude by comparing our forecasts for the senatorial and gubernatorial races in the U.S. midterm elections of 6 November 2018 with those of popular pollsters. This is joint work with Daniel Linder (Augusta Univ.), Mason Porter (UCLA), and Grzegorz Rempala (Ohio State Univ.)

Tue Oct 15

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Oct 15

## IMA Data Science Lab Seminar

12:30pm - Lind 305
Simple Approaches to Complicated Data Analysis
Deanna Needell, University of California, Los Angeles
##### Abstract:

Recent advances in technology have led to a monumental increase in large-scale data across many platforms. One mathematical model that has gained a lot of recent attention is the use of sparsity. Sparsity captures the idea that high dimensional signals often contain a very small amount of intrinsic information. Using this notion, one may design efficient low-dimensional representations of large-scale data as well as robust reconstruction methods for those representations. Binary, or one-bit, representations of data for example, arise naturally in many applications, and are appealing in both hardware implementations and algorithm design. In this talk, we provide a brief background to sparsity and 1-bit measurements, and present new results on the problem of data classification with low computation and resource costs. We illustrate the utility of the proposed approach on recently acquired data about Lyme disease.

Tue Oct 15

## Climate Seminar

11:15am - Vincent Hall 570
Climate and Non-Smooth Dynamics
Cameron Thieme, School of Mathematics
Mon Oct 14

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Oct 14

## Student Number Theory Seminar

3:35pm - Vincent Hall 1
Arithmetic Speculation on a Combinatorial Lemma
Eric Stuckey
##### Abstract:

Reflection groups are an object in classical geometry with deep connections to Lie theory, representation theory, algebraic geometry, invariant theory, and combinatorics. The first half of the talk will give a quick introduction to various flavors of reflection groups. In the second half of the talk I will state a lemma about a restricted class of reflection groups, and discuss an idea for how incorporating cyclotomic fields may allow us to remove that restriction.

Mon Oct 14

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied and Computational Mathematics Seminar

Mon Oct 14

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Oct 14

## Topology Seminar

2:30pm - Ford Hall 110
Second order terms in arithmetic statistics
Craig Westerland, University of Minnesota
##### Abstract:

The machinery of the Weil conjectures often allows us to relate the singular cohomology of the complex points of a scheme to the cardinality of its set of points over a finite field. When we apply these methods to a moduli scheme, we obtain an enumeration of the objects the moduli parameterizes. It's rare that we can actually fully compute the cohomology of these moduli spaces, but homological stability results often give a first order approximation to the homology.

In this talk, we'll explain how to obtain second order homological computations for a class of Hurwitz moduli spaces of branched covers; these yield second order terms in enumerating the moduli over finite fields. We may interpret these as second order terms in a function field analogue of the function which counts number fields, ordered by discriminant. Our second order terms match those of Taniguchi-Thorne/Bhargava-Shankar-Tsimerman in the cubic case, and give new predictions in other Galois settings.

This is joint (and ongoing) work with Berglund, Michel, and Tran.

Mon Oct 14

## Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Oct 11

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Oct 11

## Combinatorics Seminar

3:30pm - Vincent Hall 570
Kazhdan-Lusztig Immanants for k-Positive Matrices
Sunita Chepuri
##### Abstract:

Immanants are matrix functionals that generalize the determinant. One notable family of immanants are the Kazhdan-Lusztig immanants. These immanants are indexed by permutations and are defined as sums involving Kazhdan-Lusztig polynomials. One notable property of Kazhdan-Lustzig immanants is that they are nonnegative on totally positive matrices. We give a condition on permutations that allows us to extend this theorem to the setting of k-positive matrices. We also conjecture a larger class of permutations for which our theorem holds true.

Fri Oct 11

## Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri Oct 11

## Reading Seminar on Automorphic Forms

1:30pm - Vincent Hall 1
Reading Seminar on Automorphic Forms

Fri Oct 11

## Special Events and Seminars

1:25pm - Vincent Hall 213
Trace Formula (continued)
Steven Sperber, University of Minnesota
Fri Oct 11

## IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Data Science in Healthcare
Yinglong Guo, UnitedHealth Group
##### Abstract:

UnitedHealth Group Research and Development (UHG R&D) is working on creating, validating, testing, and refining innovations in the healthcare industry. Our data science team provides technical solutions by applying various statistical and machine learning methods to a vast amount of data in order to answer research questions. In this talk, I will give a brief introduction to my day-to-day experience as a data scientist. I will also discuss the methodology involved in several analyses of treatment outcomes for prostate cancer.

Thu Oct 10

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Oct 10

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Oct 10

## Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
Mike Loper, University of Minnesota
Thu Oct 10

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Oct 09

## Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Oct 09

## PDE Seminar

3:35pm - Vincent Hall 570
Diffusion in the Mean for a Periodic Schrödinger Equation Perturbed by a Fluctuating Potential
Shiwen Zhang, UMN
##### Abstract:

We consider the solution to a tight-binding, periodic Schrödinger equation with a random potential evolving stochastically in time. If the potential evolves according to a stationary Markov process we obtain a positive, finite diffusion constant for the evolution of the solution. More generally, we show that the square amplitude of the wave packet, after diffusive rescaling, converges to a solution of the heat equation. (Joint work with J. Schenker and Z. Tilocco at the Michigan State University).

Wed Oct 09

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Oct 08

## Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Oct 08

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Oct 08

## Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Oct 08

## IMA Data Science Lab Seminar

1:25pm - Lind 305
LectureParallel Transport Convolutional Neural Networks on Manifolds
Rongjie Lai, Rensselaer Polytechnic Institute
##### Abstract:

Convolution has played a prominent role in various applications in science and engineering for many years. It is also the most important operation in convolutional neural networks (CNNs). There has been a recent growth of interests of research in generalizing CNNs on 3D objects, often represented as compact manifolds. However, existing approaches cannot preserve all the desirable properties of Euclidean convolutions, namely compactly supported filters, directionality, transferability across different manifolds. In this talk, I will discuss our recent work on a new way of defining convolution on manifolds via parallel transport. This geometric way of defining parallel transport convolution (PTC) provides a natural combination of modeling and learning on manifolds. PTC allows for the construction of compactly supported filters and is also robust to manifold deformations. I will demonstrate its applications to shape analysis using deep neural networks based on parallel transportation convolutional networks (PTC-net).

Dr. Rongjie Lai received his Ph.D. degree in applied mathematics from the University of California, Los Angeles, He is currently an assistant professor at the Rensselaer polytechnic Institute. Dr. Lais research interests are mainly in modern scientific computing including developing mathematical and computational tools for analyzing and processing signals, images as well as unorganized data using methods of variational partial differential equations, computational differential geometry and learning. In 2018, Dr. Lai was granted an NSF CAREER award for his research in geometry and learning for manifold-structured data in 3D and higher dimension.

Tue Oct 08

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Oct 08

## Climate Seminar

11:15am - Vincent Hall 570
Permafrost Response to Climate Change via Budykos Model
Richard McGehee, UMN
Mon Oct 07

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Nonuniqueness in Dynamical Systems
Richard McGehee, University of Minnesota
##### Abstract:

Discontinuous vector fields arise naturally in some applications. In this presentation, a simple classical model of ocean circulation is introduced as an example of how discontinuities give rise to nonunique solutions. Standard bifurcation techniques often fail when the vector field is not smooth, and certainly fail when the vector field is discontinuous. However, some topological techniques seem to carry over, and a crude birfurcation theory can be extended to a large class of discontinuous systems.

Mon Oct 07

## Student Number Theory Seminar

3:35pm - Vincent Hall 1
A Tour of the p-adic Representation Theory of GL_2
Katy Weber
##### Abstract:

We summarize the classification of representations of GL_2 over a p-adic field, emphasizing the relationship between these representations and automorphic forms and L-functions. Time permitting, we will also discuss Whittaker models of these representations and the Casselman-Shalika formula. This talk is meant to be a sketch of these results and how they fit into the bigger picture, and should be accessible even if you are not very familiar with representation theory.

Mon Oct 07

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied and Computational Mathematics Seminar

Mon Oct 07

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Oct 07

## Topology Seminar

2:30pm - Ford Hall 110
Topology Seminar

Mon Oct 07

## Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Oct 04

## MCFAM Seminar

5:30pm - Vincent Hall 16
RANDOM RULES AND THE ANCIENT HISTORY OF SIMULATION
Arkady Shemyakin, University of St. Thomas&nbsp;
##### Abstract:

Modern approaches to simulation, involving Monte Carlo methods and randomized procedures of decision-making, are usually dated back to the mid-20th century and the arrival of the computer era. Deeper history goes back to the 19th and even 18th centuries and involves such devices as Galtons board and Buffons needle. However, one can argue that long before the invention of computers, older devices such as dice and their predecessors have been effectively used for games and divination. The idea of this paper is to review the use of ancient randomizing devices to trace the history of simulation and random rules of decision-making. Special attention will be paid to some contemporary cultures, which have preserved some unique elements of their ancient history: native cultures of the Americas, the Celtic civilizations of Ireland and Scotland, and the indigenous peoples of Northern and Central Asia (Altai and Siberia).Bio: https://www.stthomas.edu/mathematics/faculty/arkady-shemyakin.html

Fri Oct 04

## Probability Seminar

3:30pm - Vincent Hall 311
Invertibility of inhomogenuous heavy-tailed matrices
Galyna Livshyts, Georgia Tech
##### Abstract:

We will show the sharp estimate on the behavior of the smallest singular value of random matrices under very general assumptions. One of the key steps in the proof is a result about the efficient discretization of the unit sphere in an n-dimensional euclidean space. This result allows us to work with very general random matrices. The proof of the result will be outlined. Partially based on the joint work with Tikhomirov and Vershynin.

Fri Oct 04

## Combinatorics Seminar

3:30pm - Vincent Hall 570
Higher cluster categories and QFT dualities
Gregg Musiker
##### Abstract:

We present a unified mathematical framework that elegantly describes minimally supersymmetric gauge theories in various dimensions, and their dualities. Though this approach utilizes higher Ginzburg algebras and higher cluster categories (also known as m-cluster categories), we show that the constructions can be given explicitly and combinatorially. We emphasize the connections to cluster algebras and two classes of examples: one class related to toric geometry and giving rise to brane bricks, which are 3-dimensional analogues of certain bipartite graphs on surfaces, and one class corresponding to higher partial triangulations of surfaces. This is based on joint work with Sebastian Franco of City College of New York. No prior knowledge of Quantum Field Theories or Cluster Algebras will be assumed.

Fri Oct 04

## Probability Seminar

2:30pm - Vincent Hall 311
Reconstruction problems on amenable graphs
Ahmed El Alaoui, Stanford University
##### Abstract:

We consider the problem of reconstructing a hidden assignment of random variables (x_1,, x_n) sitting on the nodes of a graph, given noisy observations of pairs (x_u, x_v) for every edge (u,v) of the graph. Such problems have been extensively studied when the underlying graph is mean-field (e.g., the complete graph, Erdos-Renyi, random regular,), in which case the existence of a possible-but-hard phase where reconstruction is possible but computationally difficult is ubiquitous.

In contrast, the picture is dramatically different when the graph is amenable. I will represent a generic result about the optimality of local algorithms for computing marginals under a somewhat strong model of side information. Next, I will focus on Z_2 synchronization (aka planted Ising model) on the Euclidean lattice with weaker side information, and discuss a renormalization-based procedure for reconstructing the assignment.

Joint work with Andrea Montanari.

Fri Oct 04

## Reading Seminar on Automorphic Forms

1:30pm - Vincent Hall 1
Reading Seminar on Automorphic Forms

Fri Oct 04

## Special Events and Seminars

1:25pm - Vincent Hall 213
"Trace Formula, I"
Steven Sperber, University of Minnesota
Thu Oct 03

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Oct 03

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Oct 03

## Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Linkage, and the licci conjecture on grade 3 perfect ideals
Mahrud Sayrafi, University of Minnesota
##### Abstract:

Let Q be a regular local ring. An ideal I in Q is said to be licci if it is in the linkage class of a complete intersection. Christensen, Veliche and Weyman conjectured that a perfect ideal of grade 3 in Q is licci if and only if its free resolution corresponds to Dynkin diagrams.

After introducing the theory of linkage, I will talk about the conjecture, how Dynkin diagrams are involved, and their approach in showing one direction of the conjecture in arXiv:1712.04016.

Thu Oct 03

## IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Language and Interaction in Minecraft
Arthur Szlam, Facebook
##### Abstract:

I will discuss a research program aimed at building a Minecraft assistant, in order to facilitate the study of agents that can complete tasks specified by dialogue, and eventually, to learn from dialogue interactions. I will describe the tools and platform we have built allowing players to interact with the agents and to record those interactions, and the data we have collected. In addition, I will describe an initial agent from which we (and hopefully others) can iterate.

Thu Oct 03

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Oct 02

## Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Oct 02

## PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Wed Oct 02

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Oct 01

## Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Oct 01

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Oct 01

## Dynamical Systems

2:30pm - Vincent Hall 209
Relative equilibrium configurations of gravitationally interacting rigid bodies
Rick Moeckel, University of Minnesota
##### Abstract:

Consider a collection of n rigid, massive bodies interacting according to their mutual gravitational attraction. A relative equilibrium motion is one where the entire configuration rotates rigidly and uniformly about a fixed axis  all of the bodies are phase locked. Such a motion is possible only for special positions and orientations of the bodies. A minimal energy motion is one which has the minimum possible energy in its fixed angular momentum level. While every minimal energy motion is a relative equilibrium motion, the main result here is that a relative equilibrium motion of n >= 3 disjoint rigid bodies is never an energy minimizer. Since energy minimizers are the expected final states produced by tidal interactions, phase locking of 3 or more bodies will not occur.

Tue Oct 01

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Citizen Science and Machine Learning at Zooniverse
Darryl Wright, University of Minnesota, Twin Cities
##### Abstract:

As researchers gather ever-larger datasets there is an increasing demand for citizen science and reliance on machine learning. We will introduce Zooniverse, the world's largest citizen science platform, and show how citizen scientists are helping researchers extract meaningful information from their data. But the demand for citizen scientists and the volumes of data they are being asked to process is beginning to tax even the abilities of our 1.8 million volunteers. We will show how machine learning is being deployed to ease some of this burden and show how machine learning and citizen science can empower each other to process data more efficiently than either alone.

Tue Oct 01

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Oct 01

## Climate Seminar

11:15am - Vincent Hall 570
"An Introduction to Budyko's Energy Balance Model"
Richard McGehee
Mon Sep 30

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Sep 30

## Student Number Theory Seminar

3:35pm - Vincent Hall 1
Leading up to Dirichlets class number formula
Dev Hegde
##### Abstract:

The talk will give a historical introduction to number theory leading up to Dirichlets class number formula which was one of the biggest achievements of analytic methods in number theory. No background is necessary to understand the talk.

Mon Sep 30

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied and Computational Mathematics Seminar

Mon Sep 30

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Sep 30

## Topology Seminar

2:30pm - Ford Hall 110
Mysterious Duality
Sasha Voronov, University of Minnesota
##### Abstract:

Mysterious Duality was discovered by Iqbal, Neitzke, and Vafa in 2001. They noticed that toroidal compactifications of M-theory lead to the same series of combinatorial objects as del Pezzo surfaces do, along with numerous mysterious coincidences: both toroidal compactifications and del Pezzo surfaces give rise to the exceptional series E_k; the U-duality group corresponds to the Weyl group W(E_k), arising also as a group of automorphisms of the del Pezzo surface; a collection of various M- and D-branes corresponds to a set of divisors; the brane tension is related to the area of the corresponding divisor, etc. The mystery is that it is not at all clear where this duality comes from. In the talk, I will present another series of mathematical objects: certain versions of multiple loop spaces of the sphere S^4, which are, on the one hand, directly connected to M-theory and its combinatorics, and, on the hand, possess the same combinatorics as the del Pezzo surfaces. This is a report on an ongoing work with Hisham Sati.

Mon Sep 30

## Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Sep 27

## MCFAM Seminar

5:30pm - Vincent Hall 16
Positive Matrices and Derivative Models
Carlos Tolmasky, University of Minnesota&nbsp;
##### Abstract:

Principal components analysis has become widely used in a variety of fields. In finance and, more specifically, in the theory of interest rate derivative modeling, its use has been pioneered by R. Litterman and J. Scheinkman. Their key finding was that a few components explain most of the variance of treasury zero-coupon rates and that the first three eigenvectors represent level, slope and curvature changes on the curve. This result has been, since then, observed in various markets.Over the years, there have been several attempts at modeling correlation matrices displaying the observed effects as well as trying to understand what properties of the those matrices are responsible for the effect. Using recent results of the theory of positive matrices we characterize these matrices and, as an application, we shed light on some of the critiques to this methodology.Bio: http://mcfam.math.umn.edu/people/carlos-tolmasky

Fri Sep 27

## Combinatorics Seminar

3:30pm - Vincent Hall 570
A positivity phenomenon in Elser's Gaussian-cluster percolation model
Galen Dorpalen-Barry, University of Minnesota
##### Abstract:

Veit Elser proposed a random graph model for percolation in which physical dimension appears as a parameter. Studying this model combinatorially leads naturally to the consideration of numerical graph invariants which we call \textit{Elser numbers} \text{els}_k(G), where G is a connected graph and k a nonnegative integer. Elser had proven that \text{els}_1(G)=0 for all G. By interpreting the Elser numbers as Euler characteristics of appropriate simplicial complexes called \emph{nucleus complexes}, we prove that for all graphs G, they are nonpositive when k=0 and nonnegative for k\geq2. The last result confirms a conjecture of Elser. At the end, we will present an open problem naturally arising from our proof of Elser's conjecture.

Fri Sep 27

## Probability Seminar

2:30pm - Vincent Hall 311
Random matrices, operators and analytic functions
Benedek Valko, UW Madison
##### Abstract:

The finite circular beta-ensembles and their point process scaling limit can be represented as the spectra of certain random differential operators. These operators can be realized on a single probability space so that the point process scaling limit is a consequence of an operator level limit. The construction allows the derivation of the scaling limit of the normalized characteristic polynomials of the finite models to a random analytic function. I will review these representations and constructions, and present a couple of applications.

Joint with B. Virág (Toronto).

Fri Sep 27

## Reading Seminar on Automorphic Forms

1:30pm - Vincent Hall 1
Reading Seminar on Automorphic Forms

Fri Sep 27

## Special Events and Seminars

1:25pm - Vincent Hall 213
A p-adic analytic interpolation of a finite field character, II
Steven Sperber, University of Minnesota
Fri Sep 27

## IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Sampling from an Alternate Universe: Overview of Privacy-preserving Synthetic Data
Christine Task, Knexus Research Corporation
##### Abstract:

Data accessibility is important--publicly available data-sets support vital social science research, social programs and data-informed governance. In recent years, an increasing amount of data has been curated and made generally available through sites like data.gov, IPUMS, and other resources, fueling the progress of research in Big Data. However, data with the most potential value for public good can also be the most privacy sensitive--such as data on abuse, STDS, extreme poverty, or mental health. These datasets exist, but may be redacted or entirely withheld from public view due to legal restrictions and the very real danger that anonymized individuals may be reidentified.

Privacy-preserving synthetic data provides a pathway to publicly release datasets that contain very sensitive information. The basic process consists of three parts: A generative model is built which captures the distribution of the original sensitive data, perturbation steps are applied to the model to improve its privacy properties (either formal or heuristic-based), and then the model is used to synthesize a new data set of synthetic individuals. The synthetic dataset preserves the significant properties of the original data, but because it contains no real people, it can be safely released to the public. When the distributional difference between the real and synthetic data mimics the difference between two subsamples of the original data, i.e. when privacy error mimics sampling error, we can think of the synthetic data as survey results from a parallel dimension: The same pattern of information as the original data, with no real people.

In this talk, I'll cover approaches to creating synthetic data, the difference between formal and heuristic-based privacy, and, importantly, quality metrics used to verify that the synthetic data is a good substitute for the original data (a challenging problem itself in a high dimensional feature space). High quality synthetic data is a rapidly progressing research area, with both promising success stories and an exciting frontier of open problems.

Thu Sep 26

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Sep 26

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Sep 26

## Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Global Sections of Toric Vector Bundles
Jorin Schug
##### Abstract:

This talk will continue to follow the "Parliament of Polytopes" paper by Di Rocco, Jabbusch, and Smith. I'll discuss the result that the T-equivariant generators for the global sections of a toric vector bundle E correspond to the lattice points in the parliament of polytopes for E and look to understand this result for some examples, including direct sums of line bundles.

Thu Sep 26

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Sep 25

## PDE Seminar

3:35pm - Vincent Hall 570
Random Tug of War games for the p-Laplacian
Marta Lewicka, University of Pittsburgh
##### Abstract:

We propose a new dynamic programming principle related to the Dirichlet problem for the homogeneous p-Laplace equation in connection with the Tug of War games with noise. We also discuss similar approximations in presence of the Robin boundary conditions. For the proofs, we use martingale techniques involving various couplings of random walks and yielding estimates on the involved probabilistic representations.

Wed Sep 25

## Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Sep 25

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Sep 24

## Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Sep 24

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Sep 24

## Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Sep 24

## IMA Data Science Lab Seminar

1:25pm - Lind 305
The Geometry of Ambiguity in One-dimensional Phase Retrieval
Dan Edidin, University of Missouri
##### Abstract:

The phase retrieval problem is the problem of reconstructing an unknown signal from its Fourier intensity function. This problem has a long history in physics and engineering and occurs in contexts such as X-ray crystallography, speech processing and computational biology. As stated, the phase retrieval problem is ill-posed as there may be up to $2^N$ non-equivalent signals (called ambiguities) with the same Fourier intensity function. To enforce uniqueness additional constraints must be imposed.

In this talk we discuss the geometry of the space of ambiguities obtained by varying the signal. By understanding this geometry we prove a general result characterizing constraints that enforce a unique solution to the phase retrieval problem. This result was applied in work with Tamir Bendory and Yonina Eldar on blind phaseless short-time Fourier transform recovery.

Tue Sep 24

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Sep 24

## Climate Seminar

11:15am - Vincent Hall 570
An Introduction to Planetary Energy Balance
Richard McGehee, University of Minnesota
Mon Sep 23

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Sep 23

## Student Number Theory Seminar

3:35pm - Vincent Hall 1
Elliptic Curves
Claire Frechette
Mon Sep 23

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied and Computational Mathematics Seminar

Mon Sep 23

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Sep 23

## Topology Seminar

2:30pm - Ford Hall 110
Homology class of Deligne-Lusztig varieties
Dongkwan Kim, University of Minnesota
##### Abstract:

Since first defined by Deligne and Lusztig, a Deligne-Lusztig variety has become unavoidable when studying the representation theory of finite groups of Lie type. This is a certain subvariety of the flag variety of the corresponding reductive group, and its cohomology groups are naturally endowed with the action such finite groups, which in turn gives a decomposition of irreducible representations called Lusztig series. In this talk, I will briefly discuss the background of Deligne-Lusztig theory and provide a formula to calculate the homology class of Deligne-Lusztig varieties in the Chow group of the flag variety. If time permits, I will also discuss their analogues.

Mon Sep 23

## Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Sep 20

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Student Research - Outcome analysis of Indexed Universal Life Insurance based on Monte Carlo Simulation
Songyu Yan and Ian Luo, University of Minnesota
##### Abstract:

Indexed Universal Life (IUL) Insurance was developed to harness thepower of equity market returns with downside protection. However IUL iscurrently illustrated using a static credited rate which masks market returnvolatility inherent in its structure. As a result, what policyholders see as expectedperformance maybe far from reality in many cases. In our research, we modeledthe pricing algorithms of major IUL products and applied scenario testing usingMonte Carlo simulation of indices used in IUL products. The statistical variance ofindices leads to vastly different results than what is currently demonstrated inmany cases, and this variance may cause the failure of the policy. Our researchindicates a better method for demonstrating policy performance would be basedon an outcome analysis rather than the static method currently in use.Bios: Songyu Yan: https://www.linkedin.com/in/songyu-yan-826bb2126/          Ian Luo: https://www.linkedin.com/in/yifei-luo-9051b1170/

Fri Sep 20

## Combinatorics Seminar

3:30pm - Vincent Hall 570
Cyclic Sieving for planet partitions and symmetry
Sam Hopkins., University of Minnesota
##### Abstract:

The cyclic sieving phenomenon of Reiner, Stanton, and White says that we can often count fixed points for a cyclic group acting on a combinatorial set by plugging roots of unity into a polynomial related to this set. One of the most impressive instances of the cyclic sieving phenomenon is a theorem of Rhoades asserting that the set of plane partitions in a rectangular box under the action of promotion exhibits cyclic sieving. In Rhoades's result the sieving polynomial is the size generating function for these plane partitions, which has a well-known product formula due to MacMahon. We extend Rhoades's result by studying the interaction of promotion with symmetries of plane partitions. We obtain cyclic sieving-like formulas in this context where the relevant polynomial is the size generating function for symmetric plane partitions, whose product formula was conjectured by MacMahon and proved by Andrews. We then go on to consider the way the symmetries interact with rowmotion, another operator acting on plane partitions which is closely related to promotion. We end by explaining the connection of our work to some earlier conjectures we made concerning rowmotion acting on the P-partitions of various triangular posets P.

Fri Sep 20

## Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri Sep 20

## Reading Seminar on Automorphic Forms

1:30pm - Vincent Hall 1
Reading Seminar on Automorphic Forms

Fri Sep 20

## Special Events and Seminars

1:25pm - Vincent Hall 213
A p-adic analytic interpolation of a finite field character
Steven Sperber, University of Minnesota
Fri Sep 20

## IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 409
SIAM Industrial Panel
-, -
Thu Sep 19

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Sep 19

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Sep 19

## Colloquium

3:35pm - Vincent Hall 16
The Langlands Program: An Introduction and Recent Progress
Solomon Friedberg,, Boston College
##### Abstract:

The Langlands Program, connecting algebra, analysis and geometry in diverse ways, is foundational to modern number theory. I will introduce this program and indicate some recent progress. As we shall see, a great deal still remains to be done.

Thu Sep 19

## Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar

Thu Sep 19

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
D=4, N=1 Compactifications of Maximal Supergravities via Generalised Geometry - Kahler potentials, superpotentials and moduli
David Tennnyson, Imperial College London
##### Abstract:

We analyse compactifications of 11 dimensional or type II supergravity down to 4 dimensional Minkowski space for generic flux and generic internal Killing spinors. We note the failure of conventional differential geometry to capture the generic features of the theory and show that the correct formalism comes in the form of a closed form Leibniz algebroid - or as we call it in the physics community, generalised geometry. Our structure is similar to the generalised geometry of Hitchin, but now the structure group is the non-compact exceptional group E_{7(7)}x R^{+}. It turns out that having N=1 supersymmetry in the effective theory on Minkowski space is equivalent to an integrable SU(7) structure on the generalised tangent bundle. We provide the tensors that define the SU(7) structure and give the integrability conditions. Finally we provide an expression for the Kahler potential on the space of structures, the superpotential of the lower dimensional theory, and we explore the moduli of these structures giving explicit answers in certain cases.

Wed Sep 18

## Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Sep 18

## PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Wed Sep 18

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Siegel's extensions of Epstein zeta functions as Eisenstein series
Paul Garrett, University of Minnesota
Tue Sep 17

## Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Sep 17

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Sep 17

## Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Sep 17

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Optimal Recovery under Approximability Models, with Applications
Simon Foucart, Texas A & M University
##### Abstract:

For functions acquired through point evaluations, is there an optimal way to estimate a quantity of interest or even to approximate the functions in full? We give an affirmative answer to this question under the novel assumption that the functions belong to a model set defined by approximation capabilities. In fact, we produce implementable linear algorithms that are optimal in the worst-case setting. We present applications of the abstract theory in atmospheric science and in system identification.

Dr. Simon Foucart earned a Masters of Engineering from the Ecole Centrale Paris and a Masters of Mathematics from the University of Cambridge in 2001. In 2006, he received his Ph.D. in Mathematics at the University of Cambridge, specializing in Approximation Theory. After two postdoctoral positions at Vanderbilt University and Université Paris 6, he joined Drexel University in 2010 before moving to the University of Georgia in 2013. Since 2015, he has been with Texas A&M University, where is now professor. His recent work focuses on the field of Compressive Sensing, whose theory is exposed in the book A Mathematical Introduction to Compressive Sensing he coauthored with Holger Rauhut. Dr. Foucarts research was recognized by the Journal of Complexity, from which he received the 2010 Best Paper Award. Dr. Foucarts current interests also include the mathematical aspects of Metagenomics, Optimization, Deep Learning and Data Science at Large

Tue Sep 17

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology

Tue Sep 17

## Climate Seminar

11:15am - Vincent Hall 570
The Scientific Case for Anthropogenic Warming II
Richard McGehee, University of Minnesota
Mon Sep 16

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Sep 16

## Student Number Theory Seminar

3:35pm - Vincent Hall 1
A Brief Introduction to L-Functions
Joe Dickinson
##### Abstract:

Like Andy's talk last week, this week will be another introductory talk; the topic is L-functions. We will start with a discussion of Dirichlet's use of L-series to show the infinitude of primes in arithmetic progressions, then proceed to how L-functions have become a major area of investigation. We will discuss only a sampling of topics, with the goal of motivating interest and setting the stage for future talks.

Mon Sep 16

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Sep 16

## Topology Seminar

2:30pm - Ford Hall 110
Transfer in the homology and cohomology of categories
Peter Webb, University of Minnesota
##### Abstract:

The cohomology of a category has many properties that extend those that are familiar when the category is a group. Second cohomology classifies equivalence classes of category extensions, first cohomology parametrizes conjugacy classes of splittings, first homology is the abelianization of the fundamental group, and second homology has a theory that extends that of the Schur multiplier. Defining restriction and corestriction maps on the homology of categories is problematic: most attempts to do this require induction and restriction functors to be adjoint on both sides, and this typically does not happen with categories. We describe an approach to defining these maps that includes all the situations where they can be defined in group cohomology, at least when the coefficient ring is a field. The approach uses bisets for categories, the construction by Bouc and Keller of a map on Hochschild homology associated to a bimodule, and the realization by Xu of category cohomology as a summand of Hochschild cohomology.

Mon Sep 16

## Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Sep 13

## MCFAM Seminar

5:30pm - Vincent Hall 16
MFM Alumni/Student Panel: How the MFM Prepares You to Enter the Field of Quantitative Finance
MFM Alumni/Student Panel, Master of Financial Mathematics Program (MFM)
##### Abstract:

Learn from current students and MFM alumni in industry about the benefits of this professional master program. Panelists will talk about what attracted them to the program, how to make the most of your time in the MFM and why the practical, real-world learning helps you land jobs in quantitative risk analysis, hedging, trading, portfolio management, fintech, data analytics and other jobs that are hot in the field right now.

Fri Sep 13

## Combinatorics Seminar

3:30pm - Vincent Hall 570
Combinatorics Seminar

Fri Sep 13

## Probability Seminar

2:30pm - Vincent Hall 311
Critical behavior for percolation on graphs with given degrees
Souvik Dhara, MIT
##### Abstract:

We discuss critical behavior of percolation on finite random networks. In a seminal paper, Aldous (1997) identified the scaling limit for the component sizes in the critical window of phase transition for the Erdos-Renyi random graph (ERRG). Subsequently, there has been a surge in the literature, revealing several interesting scaling limits of these critical components, namely, the component size, diameter, or the component itself when viewed as a metric space. Fascinatingly, when the third moment of the asymptotic degree distribution is finite, many random graph models have been shown to exhibit a universality phenomenon in the sense that their scaling exponents and limit laws are the same as the ERRG. In contrast, when the asymptotic degree distribution is heavy-tailed (having an infinite third moment), the limit law turns out to be fundamentally different from the ERRG case and in particular, becomes sensitive to the precise asymptotics of the highest degree vertices.

In this talk, we will focus on random graphs with a prescribed degree sequence. We start by discussing recent scaling limit results, and explore the universality classes that arise from heavy-tailed networks. Of particular interest is a new universality class that arises when the asymptotic degree distribution has an infinite second moment. Not only it gives rise to a completely new universality class, it also exhibits several surprising features that have never been observed in any other universality class so far.

This is based on joint works with Shankar Bhamidi, Remco van der Hofstad, Johan van Leeuwaarden and Sanchayan Sen.

Fri Sep 13

## Reading Seminar on Automorphic Forms

1:30pm - Vincent Hall 1
Reading Seminar on Automorphic Forms

Fri Sep 13

## Special Events and Seminars

1:25pm - Vincent Hall 213
"p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions
TBA
Fri Sep 13

9:30am -
CANCELLED

Thu Sep 12

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Sep 12

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Sep 12

## Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar

Thu Sep 12

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology

Wed Sep 11

## Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Sep 11

## PDE Seminar

3:35pm - Vincent Hall 570
Parabolic problems with rough coefficients
Pierre Portal,, Australian National University
##### Abstract:

Using form methods, one can solve linear parabolic PDE in divergence form with $L^2$ data in appropriate energy spaces, even when the coefficients are merely bounded measurable in time and space, and no maximum principle is available. This goes back, at least, to the work of Lions and his school in the 1950s. When dealing with $L^p$ data, it is not so clear which $L^p$ like solution space one should use as a replacement of Lions energy space. Depending on the choice, one can solve, for instance, time dependent single equations (Aronson 1968), time independent systems for a range of values of $p$ (Auscher 2005), or stochastic problems with some spatial regularity (starting with Krylov 1994).
In this talk, I explain that, by choosing tent spaces as solution spaces (inspired by their role in elliptic boundary value problems on rough domains), one gets fairly general results, including both deterministic and stochastic problems, all values of $p$, systems as well as single equations, and rough coefficients in both time and space.

This summarises joint works with Pascal Auscher, Sylvie Monniaux, Jan van Neerven, and Mark Veraar.

Wed Sep 11

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Automorphic Forms and Number Theory

Tue Sep 10

## Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Sep 10

3:30pm - VinH 16
Colloquium

Tue Sep 10

## Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Sep 10

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Taming Nonconvexity: From Smooth to Nonsmooth Problems and Beyond
Ju Sun, University of Minnesota, Twin Cities
##### Abstract:

Most applied problems we encounter can be naturally written as nonconvex optimization, for which
obtaining even a local minimizer is computationally hard in theory, never mind the global minimizer. In practice, however, simple numerical methods often work surprisingly well in finding high-quality solutions, e.g., training deep neural networks.

In this talk, I will describe our recent effort in bridging the mysterious theory-practice gap for nonconvex optimization, in the context of solving practical problems in signal processing, machine learning, and scientific imaging. 1) I will highlight a family of smooth nonconvex problems that can be solved to global optimality using simple numerical methods, independent of initialization. 2) The discovery, however, does not cover nonsmooth functions, which are frequently used to encode structural objects (e.g., sparsity) or achieve robustness. I will introduce tools from nonsmooth analysis, and demonstrate how nonsmooth, nonconvex problems can also be analyzed and solved in a provable manner. 3) Toward the end, I will provide examples to show how innovative problem formulation and physical design can help to tame nonconvexity.

Ju Sun is an assistant professor at the computer science & engineering department, University of Minnesota at Twin Cities. Prior to this, he was a postdoctoral scholar at Stanford University,
working with Professor Emmanuel Cand?s. He received his Ph.D. degree from Electrical Engineering of Columbia University in 2016 (2011--2016) and B.Eng. degree in Computer Engineering (with a minor in Mathematics) from the National University of Singapore in 2008 (2004--2008). His research interests span computer vision, machine learning, numerical optimization, signal/image processing, and high-dimensional data analysis. Recently, he is particularly fascinated by why simple numerical methods often solve nonconvex problems surprisingly well (on which he maintains a bibliographic webpage: http://sunju.org/research/nonconvex/ ) and the implication on representation learning. He won the best student paper award from SPARS'15 and honorable mention of doctoral thesis for the New World Mathematics Awards (NWMA) 2017.

Tue Sep 10

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology

Tue Sep 10

## Climate Seminar

11:15am - Vincent Hall 570
"The Scientific Case for Anthropogenic Warming"
Richard McGehee, University of Minnesota
Mon Sep 09

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Emergent behavior in collective dynamics
Eitan Tadmor, University of Maryland
##### Abstract:

Collective dynamics is driven by alignment that tend to self-organize the crowd and by different external forces that keep the crowd together. Different emerging equilibria are self-organized into clusters, flocks, tissues, parties, etc.

I will overview recent results on the hydrodynamics of large-time, large-crowd collective behavior, driven by different rules of engagement. In particular, I address the question how short-range interactions lead, over time, to the emergence of long-range patterns, comparing geometric vs. topological interactions.

Mon Sep 09

## Student Number Theory Seminar

3:35pm - Vincent Hall 1
Student Number Theory Seminar

Mon Sep 09

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Sep 09

## Topology Seminar

2:30pm - Ford Hall 110
Cohomology of the space of complex irreducible polynomials in several variables
Weiyan Chen, University of Minnesota
##### Abstract:

We will show that the space of complex irreducible polynomials of degree d in n variables satisfies two forms of homological stability: first, its cohomology stabilizes as d increases, and second, its compactly supported cohomology stabilizes as n increases. Our topological results are inspired by counting results over finite fields due to Carlitz and Hyde.

Mon Sep 09

## Cockburn's Seminar

2:30pm - Ford Hall B15
Cockburn's Seminar

Fri Sep 06

## Combinatorics Seminar

3:30pm - Vincent Hall 570
Combinatorics Seminar

Fri Sep 06

## Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri Sep 06

## Reading Seminar on Automorphic Forms

1:30pm - Vincent Hall 1
Reading Seminar on Automorphic Forms

Fri Sep 06

9:30am -
CANCELLED

Thu Sep 05

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra seminar

Thu Sep 05

## Colloquium

3:35pm - Vincent Hall 16
Colloquium - Canceled
Alina Chertock, NSCU
##### Abstract:

Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.

In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxisfluid system and will also be discussed.

Thu Sep 05

## Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar

Thu Sep 05

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology

Wed Sep 04

## Student Number Theory Seminar

3:35pm - Vincent Hall 6
Student Number Theory Seminar

Wed Sep 04

## PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Tue Sep 03

## Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Sep 03

3:30pm - VinH 16
Colloquium

Tue Sep 03

## Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Sep 03

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology

Tue Sep 03

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Sep 02

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri Aug 30

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Aug 30

9:30am -
CANCELLED

Thu Aug 29

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Tue Aug 27

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Aug 26

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri Aug 23

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Aug 23

9:30am -
CANCELLED

Mon Aug 19

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri Aug 16

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Aug 16

9:30am -
CANCELLED

Wed Aug 14

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Aug 12

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Aug 12

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Aug 09

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Aug 09

9:30am -
CANCELLED

Wed Aug 07

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Aug 05

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Aug 05

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Aug 02

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Aug 02

9:30am -
CANCELLED

Wed Jul 31

## Combinatorics Seminar

3:35pm - Vincent Hall 16
Hurwitz action of reflection factorizations of Coxeter elements
Sophiane Yahiatene, Bielefeld University
##### Abstract:

In the talk we will investigate a natural braid group action on factorizations of elements in reflection groups. In particular, we will consider reflection factorizations of Coxeter elements in Coxeter groups of finite rank and state conditions whether two factorizations lie in the same orbit under the natural action. The presented result extends the investigation of Lewis - Reiner (arXiv:1603.05969) to arbitrary Coxeter groups of finite rank. (j.w. Patrick Wegener)

Wed Jul 31

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Jul 29

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jul 29

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Jul 26

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jul 26

9:30am -
CANCELLED

Wed Jul 24

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Tue Jul 23

## Combinatorics Seminar

3:35pm - Vincent Hall 113
Enumeration of bounded lecture hall tableaux
Jang Soo Kim,, Sungkyunkwan University
##### Abstract:

Recently Corteel and Kim introduced lecture hall tableaux in their study of multivariate little q-Jacobi polynomials. In this talk, we enumerate bounded lecture hall tableaux. We show that their enumeration is closely related to standard and semistandard Young tableaux. We also show that the number of bounded lecture hall tableaux is the coefficient of the Schur expansion of s?(m+y1,...,m+yn). To prove this result, we use two main tools: non-intersecting lattice paths and bijections. In particular we use ideas developed by Krattenthaler to prove bijectively the hook content formula. This is joint work with Sylvie Corteel.

Mon Jul 22

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jul 22

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Jul 19

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jul 19

9:30am -
CANCELLED

Thu Jul 18

## Combinatorics Seminar

3:35pm - Vincent Hall 16
Fibers of maps to totally nonnegative spaces and the Fomin-Shapiro Conjecture
Patricia Hersh, North Carolina State University
##### Abstract:

Anders Björner and Joseph Bernstein raised the question of finding regular CW complexes naturally arising from representation theory having the intervals of Bruhat order as their posets of closure relations. Sergey Fomin and Michael Shapiro conjectured a solution, namely the link of the identity in the totally nonnegative real part of the unipotent radical of a Borel in a semisimple, simply connected algebraic group defined and split over the reals together with a family of related spaces indexed by the different Coxeter group elements. The Fomin-Shapiro conjecture indeed proved to be true, with the proof utilizing an interpretation of these stratified spaces as images of an intriguing family of maps - maps also arising in work of Lusztig related to canonical bases. I will start by reviewing some highlights of this story, then turn to recent joint work with Jim Davis and Ezra Miller regarding the structure of the fibers of these same maps.

Wed Jul 17

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Jul 15

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jul 15

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Jul 12

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jul 12

9:30am -
CANCELLED

Wed Jul 10

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Jul 08

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jul 08

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Jul 05

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jul 05

9:30am -
CANCELLED

Wed Jul 03

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Jul 01

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jul 01

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Jun 28

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jun 28

9:30am -
CANCELLED

Wed Jun 26

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Jun 24

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jun 24

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Jun 21

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jun 21

9:30am -
CANCELLED

Wed Jun 19

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Jun 17

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jun 17

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Fri Jun 14

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jun 14

9:30am -
CANCELLED

Wed Jun 12

## Special Events and Seminars

1:30pm - Vincent Hall 364
Summer Student Representation Theory Seminar

Mon Jun 10

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jun 10

## Special Events and Seminars

1:30pm - Vincent Hall 364
Basic Operations on Representations
Andy Hardt
##### Abstract:

We continue our crash course in finite group representation theory by looking at some important operations on representations.

We start by defining the group algebra of a finite group; group representations naturally biject with modules over the group algebra.

After that, we'll talk through a variety of ways to construct new representations from old, such as restriction, induction, inflation, tensor product, and we may even squeeze in symmetric and exterior powers.

Fri Jun 07

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri Jun 07

9:30am -
CANCELLED

Thu Jun 06

## Combinatorics Seminar

3:35pm - Vincent Hall 113
Chicken Nuggets and Numerical Semigroups
Ayomikun Adeniran, Texas A&M
##### Abstract:

A numerical semigroup is a subset of N that is closed under addition, contains 0 and has finite complement in N. There are several fundamental invariants of a numerical semigroup S among which are the Frobenius number and genus of S, denoted F(S) and g(S), respectively. The quotient of a numerical semigroup S by a positive integer d is the set S/d={x|dx?S} which is also a numerical semigroup. In this talk, I will present some recent results showing the relation between the genus of S/d and the genus of S. If time permits, we will also talk about identities relating the Frobenius numbers and the genus of quotients of numerical semigroups that are generated by certain types of arithmetic progressions. This is joint work with S. Butler, C. Defant, Y. Gao, P.E. Harris, C. Hettle, Q. Liang, H. Nam, and A. Volk.

Wed Jun 05

## Special Events and Seminars

2:00pm - Vincent Hall 570
AWM Talk
Mimi Boutin
Tue Jun 04

## Special Events and Seminars

3:35pm - Vincent Hall 113
Special Events and Seminars

Tue Jun 04

## Combinatorics Seminar

3:35pm - Vincent Hall 113
Counting core partitions and numerical semigroups using polytopes
Hayan Nam, University of California at Irvine
##### Abstract:

A partition is an aa-core partition if none of its hook lengths are divisible by aa. It is well known that the number of aa-core partitions is infinite and the number of simultaneous (a,b)(a,b)-core partitions is a generalized Catalan number if aa and bb are relatively prime. In the first half of the talk, we give an expression for the number of simultaneous (a1,a2,,ak)(a1,a2,,ak)-core partitions that is equal to the number of integer points in a polytope. In the second half, we discuss objects closely related to core partitions, called numerical semigroups, which are additive monoids that have finite complements in the set of non-negative integers. For a numerical semigroup SS, the genus of SS is the number of elements in ??SN?S and the multiplicity is the smallest nonzero element in SS. In 2008, Bras-Amorós conjectured that the number of numerical semigroups with genus gg is increasing as gg increases. Later, Kaplan posed a conjecture that implies Bras-Amorós conjecture. In this talk, we prove Kaplan's conjecture when the multiplicity is 4 or 6 by counting the number of integer points in a polytope. Moreover, we find a formula for the number of numerical semigroups with multiplicity 4 and genus gg.

Mon Jun 03

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri May 31

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
TBA
Fri May 31

9:30am -
CANCELLED

Wed May 29

## Special Events and Seminars

1:30pm - Vincent Hall 206
Informal Fluids Seminar
Raj Beekie
Mon May 27

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri May 24

9:30am -
CANCELLED

Tue May 21

## Math Physics Seminar

12:20pm - Vincent Hall 209
Second quantization of elliptic Calogero-Sutherland models
Bjorn Berntson
##### Abstract:

Calogero-Sutherland models are a class of completely integrable (quantum) many-body systems. In the most general case, particles interact pairwise through an elliptic potential. We discuss the second quantization of several elliptic Calogero-Sutherland models. In degenerate (trigonometric, rational) cases, there is a well-studied correspondence between Calogero-Sutherland systems and Benjamin-Ono equations, a nonlinear, integrable integro-differential equation. We discuss the correspondence in the elliptic regime, where second quantization of a particular system leads to a new two-component elliptic Benjamin-Ono equation. We construct a Lax pair for this equation via a Riemann-Hilbert problem on the torus. This is joint work with Edwin Langmann and Jonatan Lenells.

Mon May 20

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri May 17

9:30am -
CANCELLED

Thu May 16

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu May 16

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Tue May 14

## Special Events and Seminars

3:30pm - Vincent Hall 570
Singularity formation for some solutions of the incompressible Euler equation
Tarek Elgindi
##### Abstract:

We describe a recent construction of self-similar blow-up solutions of the incompressible Euler equation. A consequence of the construction is that there exist finite-energy $C^{1,a}$ solutions to the Euler equation which develop a singularity in finite time for some range of $a>0$. The approach we follow is to isolate a simple non-linear equation which encodes the leading order dynamics of solutions to the Euler equation in some regimes and then prove that the simple equation has stable self-similar blow-up solutions.

Tue May 14

## Math Physics Seminar

12:30pm - Vincent Hall 209
3rd order symmetries for systems on the 2-sphere and the 2 two-sheet 2-hyperboloid -- Superintegrability and cubic algebras
Willard Miller, University of Minnesota (Joint with Ian Marquette, University of Queensland, and Bjorn Berntson, KTH Royal Institute of Techn
##### Abstract:

There are many papers concerning 3rd and higher order superintegrable systems on 2D Euclidean space, particularly by Pavel Winternitz, his students and collaborators. However, we are not aware of similar studies on nonflat spaces. We decided to study the 2-sphere (with separation in polar coordinates) and the 2-hyperboloid (with separation in horospherical coordinates). The computations were very complex for these nonflat systems and the results less rich than for flat space, which is to be expected. In each case we have a Hamiltonian operator H a 2nd order symmetry operator A and compute a 3rd order symmetry operator B.
We classified the potentials which yielded

a nonzero B. They fall into 4 classes: 1) Systems that are 2nd order superintegrable, 2) Systems that are 3rd order superintegrable but do not generate a cubic algebra, 3) Systems with algebraically dependent generators A and B, 4) Systems that are 3rd order superintegrable with a cubic algebra.

We pay special attention to the class 3 cases which also occur for Euclidian space with little change. We call these functionally dependent superintegrable systems, and show that they always permit a computation of the A eigenfunctions by simple quadrature. For the hyperboloid we show that the TTW method applied to a 2nd order
superintegrable system in horospherical coordinates yields a 3rd order superintegrable system.

Tue May 14

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Mon May 13

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri May 10

## First Year Seminar

5:30pm - Vincent 364
First Year Seminar
TBA
Fri May 10

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Facial weak order in hyperplane arrangements
Aram Dermenjian, UQAM
##### Abstract:

We discuss the facial weak order, a poset structure that extends the poset of regions on a central hyperplane arrangement to the set of all faces of the arrangement which was first introduced on the braid arrangements by Krob, Latapy, Novelli, Phan and Schwer. We provide various characterizations of this poset including a global one, a local one, one using covectors and a geometric one using the associated zonotope. We then show that the facial weak order is in fact a lattice for simplicial hyperplane arrangements, generalizing a result by Björner, Edelman and Zieglar showing the poset of regions is a lattice for simplicial arrangements. We end by stating some properties on the facial weak order.

Fri May 10

## Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri May 10

9:30am -
CANCELLED

Thu May 09

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu May 09

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu May 09

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu May 09

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Thu May 09

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Student Number Theory Seminar

Wed May 08

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Wed May 08

## AMS Intro to Research Seminar

5:20pm - Vincent Hall 570
AMS Intro to Research Seminar

Wed May 08

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Algebraic Representation Theory

Wed May 08

## PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Tue May 07

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue May 07

## Math Physics Seminar

12:20pm - Vincent Hall 209
Polytopes and elliptopes in the foundations of quantum mechanics
Michael Janas and Michel Janssen, School of Physics and Astronomy, University of Minnesota
##### Abstract:

Bell's inequality for classical correlations is perhaps the most famous result in quantum foundations. Less familiar is the so-called Tsirelson bound, for the corresponding quantum correlations. We first review Bell's inequality in its original form, where one attempts to classically simulate the following quantum experiment: Alice and Bob independently measure a spin component of one of a pair of spin-1/2 particles entangled in the singlet state. We show that the resulting set of classical and quantum correlations allowed in this setup may be visualized as a tetrahedron and an elliptope, respectively, in three-dimensional space. We then consider how to generalize these results to the case of either more settings or more outcomes (i.e., higher spin). In the case of more than two outcomes, the restrictions on the classical simulations lead to high-dimensional polytopes and highly-faceted polyhedra. In the case of four settings we arrive at the Clauser-Horne-Shimony-Holt (CHSH) inequality, a form of the Bell inequality commonly used in experimental tests. In this context, we briefly discuss connections to semi-definite programming and the topic of spectrahedral shadows.

Tue May 07

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Mon May 06

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Mon May 06

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Classical Properties of Epstein zeta functions
Adrienne Sands, University of Minnesota
Mon May 06

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
On localizing and concentrating of electromagnetic fields
Yi-Hsuan Lin, University of Jyvaskyla
##### Abstract:

We consider field localizing and concentration of electromagnetic waves governed by the time-harmonic anisotropic Maxwell system in a bounded domain. It is shown that there always exist certain boundary inputs which can generate electromagnetic fields with energy localized/concentrated in a given subdomain while nearly vanishing in another given subdomain. The theoretical results may have potential applications in telecommunication, inductive charging and medical therapy. We also derive a related Runge approximation result for the time-harmonic anisotropic Maxwell system with partial boundary data.

Mon May 06

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium

Mon May 06

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon May 06

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Robust Accelerated Gradient Methods
Mert Gurbuzbalaban, Rutgers, The State University Of New Jersey
##### Abstract:

We study the problem of minimizing a strongly convex and smooth function when we have noisy estimates of its gradient. We propose a novel multistage accelerated algorithm that is universally optimal in the sense that it achieves the optimal rate both in the deterministic and stochastic case and operates without knowledge of noise characteristics. The algorithm consists of stages that use a stochastic version of Nesterov's accelerated algorithm with a specific restart and parameters selected to achieve the fastest reduction in the bias-variance terms in the convergence rate bounds.

Mert Gürbüzbalaban is an assistant professor at Rutgers University. Previously, he was a postdoctoral associate at the Laboratory for Information and Decision Systems (LIDS) at MIT. He is broadly interested in optimization and computational science driven by applications in large-scale information and decision systems. He received his B.Sc. degrees in Electrical Engineering and Mathematics as a valedictorian from Bo?aziçi University, Istanbul, Turkey, the Diplôme dingénieur degree from École Polytechnique, France, and the M.S. and Ph.D. degrees in (Applied) Mathematics from the Courant Institute of Mathematical Sciences, New York University.

Dr. Gürbüzbalaban received the Kurt Friedrichs Prize (given by the Courant Institute of New York University for an outstanding thesis) in 2013, Bronze Medal in the École Polytechnique Scientific Project Competition in 2006, the Nadir Orhan Bengisu Award (given by the electrical-electronics engineering department of Bo?aziçi University to the best graduating undergraduate student) in 2005 and the Bülent Kerim Altay Award from the Electrical-Electronics Engineering Department of Middle East Technical University in 2001. He received funding from a variety of sources including multiple programs at the U.S. National Science Foundation.

Fri May 03

## First Year Seminar

5:30pm - Vincent 364
First Year Seminar
TBA
Fri May 03

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Combinatorics of cluster structures in Schubert varieties
Melissa Sherman-Bennett, UC Berkeley/Harvard
##### Abstract:

The (affine cone over the) Grassmannian is a prototypical example of a variety with "cluster structure"; that is, its coordinate ring is a cluster algebra. Scott (2006) gave a combinatorial description of this cluster algebra in terms of Postnikov's plabic graphs. It has been conjectured essentially since Scott's result that Schubert varieties also have a cluster structure with a description in terms of plabic graphs. I will discuss recent work with K. Serhiyenko and L. Williams proving this conjecture. The proof uses a result of Leclerc, who shows that many Richardson varieties in the full flag variety have cluster structure using cluster-category methods, and a construction of Karpman to build plabic graphs for each Schubert variety. Time permitting, I will also discuss our results on cluster structures on a larger class of positroid varieties, which involve the combinatorics of "generalized" plabic graphs.

Fri May 03

## Lie Theory Seminar

2:30pm - Vincent Hall 6
Lie Theory Seminar

Fri May 03

## Probability Seminar

2:30pm - Vincent Hall 213
The majority vote process on trees: convergence to equilibrium
Larry Gray, UMN
##### Abstract:

This is joint with Maury Bramson, who introduced our work last week and then spoke more particularly about the existence of uncountably many mutually singular equilibria in the majority vote process on a tree of vertex degree 5 and higher, whenever the noise rate is sufficiently small. Each equilibrium is associated with a different fixed point of the majority vote operation.

Natural question: If the system starts at (or near) one of these fixed points and the noise rate is small, does it converge to the corresponding equilibrium, and if so, how fast? Answering this question can tell us much about the properties of these equilibria, but standard techniques do not apply. I will describe a new method, based on the "graphical construction" of these systems, which shows exponentially quick convergence to equilibrium when the noise rate is sufficiently small. These methods apply to other models on trees, such as the stochastic Ising model, for which the convergence result was previously unknown.

This lecture is self-contained; essential features from the previous week will be included (with some new pictures).

Fri May 03 1:25pm - Lind 305
Startup vs. BigCo: Industry Experiences Compared
Ben Peirce, Samsung Research America
##### Abstract:

Choosing a career path in industry after spending years in academia can be daunting, particularly when deciding between working for a large company or a startup. In this talk, I'll discuss my experiences in both environments, and consider the pros and cons of each for people with more theoretical backgrounds.

Ben Peirce is Sr. Director of Development at Samsung Research America in Mountain View, CA, where his team builds analytics tools for mobile software services. He joined Samsung in 2018 through the acquisition of his virtual reality analytics startup, Vrtigo, where he served as CEO. Prior to co-founding Vrtigo, Ben spent a decade building analytics systems at several startups as either founder or early employee. He has a Ph.D. in engineering and S.M. in applied mathematics from Harvard, where he studied control theory and robotics, and a B.M.E. from the University of Minnesota.

Fri May 03

## Ordway Lecture Series

1:25pm - Vincent Hall 301
Representations of Real Reductive Groups
Professor Kari Vilonen, University of Melbourne
Fri May 03

9:30am -
CANCELLED

Thu May 02

## Colloquium

3:35pm - Vincent Hall 16
Singularity Formation in 3D Euler Equations and Related Models
Thomas Hou, Ordway Vsitor, Caltech
##### Abstract:

Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data is a long-standing open question in mathematical fluid dynamics. Recent computations have provided strong numerical evidence that the 3D Euler equations develop a finite time singularity from smooth initial data. I will report some recent progress in providing a rigorous justification of the singularity formation in the 3D Euler equations and related models.

Thu May 02

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu May 02

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu May 02

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Commutative Algebra Seminar

Thu May 02

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu May 02

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Thu May 02

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Introduction to Langlands philosophy
Dev Hedge, University of Minnesota
##### Abstract:

We will give less precise but hopefully very motivational introduction to Langlands philosophy with many examples. A serious background in anything is not essential.

Thu May 02

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570
Reading Seminar on Automorphic Forms

Wed May 01

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Wed May 01

## AMS Intro to Research Seminar

5:20pm - Vincent Hall 570
AMS Intro to Research Seminar

Wed May 01

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Jordan form data from the perspective of the derived category
Peter Webb, University of Minnesota
##### Abstract:

We show that certain sets of representations of Dynkin quivers are determined by their Jordan form data. The description is phrased in terms of the bounded derived category of representations of the quiver. This continues the study of the paper of Garver, Patrias and Thomas: Minuscule reverse plane partitions via quiver representations.

Wed May 01

## PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Wed May 01

## Ordway Lecture Series

1:25pm - Vincent Hall 301
Representations of Real Reductive Groups
Professor Kari Vilonen, University of Melbourne
Tue Apr 30

## Colloquium

3:35pm - Vincent Hall 16
The NTRU Class of cryptosystems, lattices, and post quantum cryptography
Jeffrey Hoffstein, Brown University
##### Abstract:

I'll discuss the nature and origins of public key cryptography, and the dangers that the development of quantum computers pose to the security of the internet and virtually all cryptosystems presently in widespread use. All public key cryptographic systems are based on a hard mathematical problem, and I'll explain how, while originally despised, hard problems based on lattices have evolved to become the most promising direction for the development of quantum resistant cryptography. I'll focus on NTRU, the earliest effective and efficient public key cryptosystem, which was developed in 1996 by myself, Jill Pipher and Joe Silverman. I will also discuss the recent history of public key cryptography. The talk will require no previous knowledge of lattices or cryptography, and will be aimed at a wide audience.

Tue Apr 30

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Apr 30

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Apr 30

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Mon Apr 29

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Mon Apr 29

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Mon Apr 29

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Applied and Computational Mathematics Seminar

Mon Apr 29

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium

Mon Apr 29

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Apr 29

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Solving Multiscale Problems with Subsampled Data by Integrating PDE Analysis with Data Science
Thomas Hou, California Institute of Technology
##### Abstract:

In many practical applications, we often need to provide solutions to quantities of interest to a large-scale problem but with only subsampled data and partial information of the physical model. Traditional PDE solvers cannot be used directly for this purpose. On the other hand, many powerful techniques have been developed in data science to represent and compress data for useful information. A crucial factor for the success of these methods is to exploit some low rank or sparsity structures in these high-dimensional data. In this talk, we will describe our recent effort in developing effective numerical methods to solve multiscale problems using subsampled data. The PDE analysis will help reveal certain important solution structures so that we can use techniques from data science to give accurate approximations for these quantities of interest.

Thomas Yizhao Hou is the Charles Lee Powell professor of applied and computational mathematics at Caltech. His research interests are centered around developing mathematical analysis and effective computational methods for vortex dynamics, interfacial flows, multiscale problems and data analysis. He received his Ph.D. in mathematics from UCLA in 1987, and joined the Courant Institute as a junior faculty member in 1989. He moved to Caltech in 1993 and was named the Charles Lee Powell Professor in 2004. He was the founding Editor-in-Chief of the SIAM Journal on Multiscale Modeling and Simulation from 2002 to 2007 and served on the IMA Board of Governors from 2010 to 2014. Dr. Hou is a Fellow of American Academy of Arts and Sciences, a SIAM Fellow and an AMS Fellow.

Mon Apr 29

## Ordway Lecture Series

1:25pm - Vincent Hall 301
Representations of Real Reductive Groups
Professor Kari Vilonen, University of Melbourne
Fri Apr 26

## First Year Seminar

5:30pm - Vincent 364
First Year Seminar
TBA
Fri Apr 26

## Lie Theory Seminar

3:35pm - Vincent Hall 6
Lie Theory Seminar

Fri Apr 26

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Generalized Bott-Samelson resolutions for Schubert varieties
Eric Sommers, UMass Amherst
##### Abstract:

This talk focuses on generalized Bott-Samelson resolutions of Schubert varieties. These resolutions are iterated G/P-bundles (for different parabolic subgroups P of the algebraic group G). Special cases have appeared in the work of Zelevinsky, Wolper, Ryan and several other authors. After introducing these resolutions and some of their properties, we discuss a possible best resolution for a given Schubert variety X(w), based on a combinatorial condition on the inversion set of the Weyl group element w. If time permits, we will discuss a computer program that calculates local intersection cohomology (i.e., Kazhdan-Lusztig polynomials) from these resolutions. This is joint work with Jennifer Koonz.

Fri Apr 26

## Ordway Lecture Series

3:35pm - Vincent Hall 6
New examples of Euler systems
Ordway Visitor Christopher Skinner, Princeton University
##### Abstract:

In this talk we will describe a number of new Euler systems and especially try to explain how the ideas from our 2nd lecture fit in. These new examples include Euler systems for Rankin-Selberg products for modular forms (due to Lei, Loeffler, and Zerbes), for Siegel modular forms of genus 2, and for products of unitary groups, among others.

Fri Apr 26

## Probability Seminar

2:30pm - Vincent Hall 213
Majority vote processes on trees
Maury Bramson, UMN
##### Abstract:

The majority vote process was one of the first interacting particle systems to be investigated and can be described as follows. There are two possible opinions at each site and that opinion switches randomly to the majority opinion of the neighboring sites. Also, at a different rate epsilon, the opinion at each site randomly changes due to noise.

Despite its simple dynamics, the majority vote process is difficult to analyze. In particular, on Z^d with d>1 and epsilon chosen small, it is not known whether there exists more than one equilibrium. This is surprising due to the close analogy between the majority vote process and the Ising model.

Here, we discuss work with Larry Gray on the majority vote process on the infinite tree with vertex degree d, where it is shown that, for small noise, there are uncountably many mutually singular equilibria, and that convergence to equilibrium occurs exponentially quickly from nearby initial states. Our methods rely on graphical constructions; they are quite flexible and can be used to obtain analogous results for other models, such as the stochastic Ising model on a tree.

This is the first part of a two-lecture presentation, and will concentrate on background and on existence of equilibria. Larry Gray will give the second part the following week, which will concentrate on convergence.

Fri Apr 26

## Special Events and Seminars

2:30pm - Vincent Hall 311
DRP End of Semester Presentations

Speaker:
Affiliation
Abstract:

Fri Apr 26

## Ordway Lecture Series

1:25pm - Vincent Hall 301
Representations of Real Reductive Groups
Professor Kari Vilonen, University of Melbourne
Fri Apr 26

9:30am -
CANCELLED

Thu Apr 25

## Colloquium

3:35pm - Vincent Hall 16
Recent progress on the Gan-Gross-Prasad and Ichino-Ikeda conjectures for unitary groups
Raphael Beuzart-Plessis, CNRS and Columbia University
##### Abstract:

A celebrated result of Waldspurger from the eighties express the central value of certain base-change L-functions for $GL_2$ as toric periods of modular forms or generalizations thereof. In the mid 2000s Gan, Gross and Prasad have formulated conjectural generalizations to higher rank classical groups relating the non-vanishing of central values of certain automorphic L-functions to the non-vanishing of certain explicit integrals of automorphic forms that are called 'automorphic periods'. These predictions have been subsequently refined by Ichino-Ikeda and N.Harris into precise identities relating the two invariants. These conjectures also have local counterparts which concern certain branching laws in the representation theory of real or p-adic groups. Most of these conjectures have now been established for unitary groups. This talk aims to give an introduction to this circle of ideas and to review recent results on the subject.

Thu Apr 25

## Special Events and Seminars

2:30pm - Vincent Hall570
DRP End of Semester Presentations

Thu Apr 25

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Harmonic surfaces and simple loops
Vlad Markovic - Ordway Visitor, Caltech
Thu Apr 25

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Apr 25

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Commutative Algebra Seminar

Thu Apr 25 1:00pm - Walter B28
Test Seminar

Thu Apr 25

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Apr 25

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Thu Apr 25

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Applying to Jobs in Number Theory
Panel, University of Minnesota
##### Abstract:

Come hear recent graduates and current grad students discuss their experiences navigating the job market. This panel is hosted by the Student Number Theory seminar, but all graduate students are welcome to attend.

Thu Apr 25

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570
Reading Seminar on Automorphic Forms

Wed Apr 24

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Wed Apr 24

## AMS Intro to Research Seminar

5:20pm - Vincent Hall 570
AMS Intro to Research Seminar

Wed Apr 24

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Heaps and minuscule posets - coontinuation
Victor Reiner, University of Minnesota
##### Abstract:

We continue reviewing minuscule weights, their weight posets, and minuscule heaps, with the goal of eventually understanding Section 4 of the paper by Garver, Patrias and Thomas

Wed Apr 24

## PDE Seminar

3:35pm - Vincent Hall 570
SERRIN LECTURE - Hydrodynamic stability and coherent structure at high Reynolds number
Jacob Bedrossian, Maryland
##### Abstract:

In this talk I will discuss recent work towards understanding certain stability questions for incompressible Euler or Navier-Stokes at high Reynolds number, the regime in which the viscous effects are weak. We will discuss the mechanisms which stabilize the most basic classes of equilbria: vortices and shear flows in 2D Navier-Stokes/Euler. These stabilization mechanisms, sometimes known as inviscid damping and enhanced dissipation arise from the skew-symmetric transport and the interaction between transport and the weak viscosity. We go on to discuss the roles such dynamics play in 3D, in particular, the manner in which two-dimensional stability can influence coherent structures in 3D. First, we discuss the subcritical transition of 3D shear flows -- the problem of obtaining quantitative estimates on the basin of stability of classical equilibria and the classification of solutions on the borderline of the stability domain. Second, the dynamics of vortex filaments in the 3D Navier-Stokes equations, which begins with understanding the local-in-time well-posedness with certain singular initial data, specifically, vorticity in a scale-invariant Morrey space of measures (in such a class, one does not have, nor does one expect, a general theory of local well-posedness). Connections to kinetic theory problems arising originally in plasma physics regarding nonlinear Landau damping will be addressed if time permits.

Wed Apr 24

## Lie Theory Seminar

1:25pm - Vincent Hall 301
A new proof of the Jacquet-Rallis fundamental lemma
Professor Raphael Beuzart-Plessis, CNRS and Columbia University
##### Abstract:

The Jacquet-Rallis fundamental lemma is a local identity between (relative) orbital integrals which originates from the relative trace formula approach to the Gan-Gross-Prasad conjecture for unitary groups and is a crucial ingredient in the recent results of W. Zhang on this conjecture. It was established soon after its formulation by Z. Yun in positive characteristic using the same geometric ideas as in Ngô's proof of the endoscopic fundamental lemma and transferred to characteristic 0 by J. Gordon by model-theoretic techniques. In this talk, I will present an alternative proof of this fundamental lemma in characteristic zero which is purely local and based on harmonic analytic tools. We note that a third proof of this fundamental lemma has been recently proposed by W. Zhang through a similar although global argument.

Tue Apr 23

## Ordway Lecture Series

3:35pm - Vincent Hall 16
Euler systems and local representation theory
Ordway Visitor Christopher Skinner, Princeton University
##### Abstract:

Many of the known examples of Euler systems come from special cycles on Shimura varieties. So algebraic groups are not far in the background. In this talk we will explain how some of the important properties of these Euler systems can be interpreted in terms of the representation theory of the corresponding groups.

Tue Apr 23

## Special Events and Seminars

3:30pm - Vincent Hall 364
Vortex filaments in the 3D Navier-Stokes equations
Jacob Bedrossian, Maryland
##### Abstract:

We consider solutions of the Navier-Stokes equations in 3d with vortex filament initial data of arbitrary circulation, that is, initial vorticity given by a divergence-free vector-valued measure of arbitrary strength supported on a smooth curve. First, we prove global well-posedness for perturbations of the Oseen vortex column in scaling-critical spaces. Second, we prove local well-posedness (in a sense to be made precise) when the filament is a smooth, closed, non-self-intersecting curve. Besides their physical interest as a model for the coherent vortex filament structures observed in 3d fluids, these results are the first to give well-posedness (in a certain sense) in a neighborhood of large self-similar solutions of 3d Navier-Stokes, as well as solutions which are locally approximately self-similar. Joint work with Pierre Germain and Benjamin Harrop-Griffiths.

Tue Apr 23

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Apr 23

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Self-homeomorphisms of reducible 3-manifolds and applications in topology, geometry and dynamics.
Christoforos Neofytidis, University of Geneva
##### Abstract:

We recall the self-homeomorphisms of a closed oriented reducible 3-manifold. Using this description, we discuss various problems in low-dimensional topology and dynamics, such as the existence of Anosov tori in 3-manifolds (joint work with Shicheng Wang), the simplicial volume of mapping tori of 3-manifolds (joint work Michelle Bucher) and the virtual Betti numbers of mapping tori of 3-manifolds.

Tue Apr 23

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Apr 23

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Mon Apr 22

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Mon Apr 22

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Classical properties of Epstein zeta functions
Adrienne Sands, University of Minnesota
##### Abstract:

Adrienne Sands of U of MN will continue on "Classical properties of Epstein zeta functions

Mon Apr 22

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Applied and Computational Mathematics Seminar

Mon Apr 22

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium

Mon Apr 22

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Apr 22

## IMA Data Science Lab Seminar

1:25pm - Lind 305
How Hard is it to Fool a Neural Net? A Mathematical Look at Adversarial Examples
Tom Goldstein, University of Maryland
##### Abstract:

Neural networks solve complex computer vision problems with human-like accuracy. However, it has recently been observed that neural nets are easily fooled and manipulated by "adversarial examples," in which an attacker manipulates the network by making tiny changes to its inputs. In this talk, I give a high-level overview of adversarial examples, and then discuss a newer type of attack called "data poisoning," in which a network is manipulated at train time rather than test time. Then, I explore adversarial examples from a theoretical viewpoint and try to answer a fundamental question: "Are adversarial examples inevitable?"

Tom is an Assistant Professor at University of Maryland. His research lies at the intersection of optimization and distributed computing, and targets applications in machine learning and image processing. He designs optimization methods for a wide range of platforms. This includes powerful cluster/cloud computing environments for machine learning and computer vision, in addition to resource limited integrated circuits and FPGAs for real-time signal processing. Before joining the faculty at Maryland, he completed his PhD in Mathematics at UCLA, and was a research scientist at Rice University and Stanford University. He has been the recipient of several awards, including SIAMs DiPrima Prize, a DARPA Young Faculty Award, and a Sloan Fellowship.

Fri Apr 19

## First Year Seminar

5:30pm - Vincent 364
First Year Seminar
TBA
Fri Apr 19

## MCFAM Seminar

5:30pm - Vincent Hall 16
2019 MFM Modeling Workshop Presentations- Yield Curve Construction and Valuation and Replication Strategies for Variance Derivatives
2019 FM Modeling Workshop Student Presenters, University of Minnesota
##### Abstract:

Two Teams of MFM students from the 2019 MFM Modeling Workshp will present their work to the Seminar. Each group will take a half hour to cover their topics, including Q & A

Yield Curve Construction: Calculating the present value of future cash flows is a crucial task for any trading desk. We will explore yield curve bootstrapping and interpolation techniques used to value financial instruments in a consistent framework. The pros and cons of each method will become apparent, and we will converge on an optimal technique that is consistent with major trading desks. Finally, we will see how the financial crisis changed yield curve construction, and fundamentally altered the way we think of the valuing future cash flows.

Valuation and Replication Strategies for Variance Derivatives:Variance derivatives have played a major role in the financial markets since the 1990s, as they provide pure exposure to volatility without other added effects. A primary instrument is variance swaps. In this project the participants will explore traditional theory of valuing variance swaps, and their continuous and discrete replication with vanilla derivatives. The connections among variance, volatility swaps, and VIX derivatives will be drawn, alongside examining non-parametric variance swap replication approaches.

Fri Apr 19

## Combinatorics Seminar

3:35pm - Vincent Hall 570
K polynomials and matroids
Andrew Berget, Western Washington University
##### Abstract:

This talk is my about 2009 UMn PhD thesis problem which I have finally solved, only 10 years after the fact. The set-up was to take n vectors, tensor them together in n! ways, and consider their span as a representation of the symmetric group Sn. The problem was to see if the character of this representation could be determined knowing only the matroid of the n starting vectors. In this talk I present an affirmative solution to this problem, including an explicit generating function that computes the character from the matroid. The long overdue solution took a lengthy detour through representation theory, algebraic geometry and, fusing the two, equivariant K-theory. I will keep the technical aspects to a minimum, and focus on explaining how this problem in combinatorics led to a tractable geometric problem.

Fri Apr 19

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Apr 19

## Probability Seminar

2:30pm - Vincent Hall 213
Optimal Spectral Shrinkage and PCA with Heteroscedastic Noise
Will Leeb, UMN
##### Abstract:

I will present recent results on the related problems of denoising, covariance estimation, and principal component analysis for the spiked covariance model with heteroscedastic noise. Specifically, I will present an estimator of the principal components based on whitening the noise, and optimal spectral shrinkers for use with these estimated principal components. I will also show new results on the optimality of whitening for principal subspace estimation. This is joint work with Elad Romanov of the Hebrew University.

Fri Apr 19

9:30am -
CANCELLED

Thu Apr 18

## Colloquium

3:35pm - Vincent Hall 16
Teichmueller flow and complex geometry of Moduli Spaces
Vlad Markovic - Ordway Visitor, Caltech
##### Abstract:

I will explain why in general the Caratheodory and Teichmueller metrics do not agree on Teichmueller spaces and why this yields a proof of the convexity conjecture of Siu. Moreover, I will illustrate how deep theorems in Teichmueller dynamics play an important role in classifying Teichmueller discs where the two metrics agree.

Thu Apr 18

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Apr 18

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry

Thu Apr 18

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Commutative Algebra Seminar

Thu Apr 18

## Ordway Lecture Series

1:25pm - Vincent Hall 113
An introduction to Euler systems
Ordway Visitor Christopher Skinner, Princeton University
##### Abstract:

The breakthrough work of Kolyvagin on the Birch and Swinnerton-Dyer conjecture introduced the method of Euler systems.' Euler systems -- when known to exist -- remain one of the most effective tools for studying class groups and Selmer groups and their relations to special values of L-functions. This is an area that has had a recent resurgence of activity, which we hope to describe in these talks. This talk will be an introduction to Euler systems and their main features.

Thu Apr 18

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Apr 18

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Thu Apr 18

## Student Number Theory Seminar

11:00am - Vincent Hall 213
More Yang-Baxter Equations for Metaplectic Ice
Claire Frechette, University of Minnesota
##### Abstract:

In preparation for my oral exam, I will extend the existing connections between quantum groups and the study of spherical Whittaker models on metaplectic covering groups of GL(r,F), for F a nonarchimedean local field. Brubaker, Buciumas, and Bump showed that for a certain metaplectic n-fold cover of GL(r,F) a set of Yang-Baxter equations govern the behavior of the Whittaker functions and that these equations arise from a Drinfeld twist of a quantum affine Lie superalgebra. I will extend their results to all metaplectic covers of GL(r,F), showing that the same Yang-Baxter equations underlie the scattering matrix for the Whittaker functions over an nQ-fold metaplectic cover, where nQ is an integer determined by the cover, and that these equations arise from Drinfeld twists of quantum groups. (I will also define what most of these words mean.)

Thu Apr 18

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570
Reading Seminar on Automorphic Forms

Wed Apr 17

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Wed Apr 17

## AMS Intro to Research Seminar

5:20pm - Vincent Hall 570
AMS Intro to Research Seminar

Wed Apr 17

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Heaps and minuscule posets
Victor Reiner, University of Minnesota
##### Abstract:

We review minuscule weights, their weight posets, and minuscule heaps, with the goal of eventually understanding Section 4 of the paper by Garver, Patrias and Thomas.

Wed Apr 17

## PDE Seminar

3:35pm - VinH 213
PDE Seminar

Wed Apr 17

## PDE Seminar

3:35pm - Vincent Hall 570
On some recent results of Collisional Plasma in bounded domains
Chanwoo Kim, University of Wisconsin
##### Abstract:

In this talk we discuss Vlasov-Poisson-Boltzmann system in bounded domains. Some recent results on regularity and large time behavior of solutions will be presented.

Tue Apr 16

## Colloquium

3:35pm - Vincent Hall 16
What's known about the Birch and Swinnerton-Dyer Conjecture
Ordway Visitor Christopher Skinner, Princeton University
##### Abstract:

The celebrated Birch and Swinnerton-Dyer (BSD) Conjecture connects the structure of the rational points on an elliptic curve defined over the rationals to the analytic properties of its associated Hasse-Weil L-function. This talk will recall the BSD conjecture (and its various parts) and related conjectures and survey some of the known results toward them, especially recent work.

This talk is intended for a general mathematical audience: no prior acquaintance with elliptic curves or even non-elementary number theory will be assumed.

Tue Apr 16

## Dynamical Systems

2:30pm - Vincent Hall 313
The Origins of the Reaction Zone in Microtornado Experiments
Patrick Shipman, Colorado State University
##### Abstract:

In experimental systems involving diffusing and convecting vapors that react to form solid particulates, a complex sequence of nucleation and growth reactions produces pulsing charged crystals, oscillating fronts, and patterns such as beautiful 3-dimensional structures that we call microtornadoes, microstalagtites, and microhurricanes. We will review the rich history of these experiments, starting with a counterdiffusional experiment that figures in the pioneering work on diffusion of Dalton, Graham, Fick, and Stefan. Mathematical analysis will progress from a reaction-diffusion model for the origins of the initial reaction zone, to an analysis of oscillations and particle size distributions, to a fluid dynamical model. The insights carry over to similar structures in protein crystallization experiments and the formation of periodic structures in plants.

Tue Apr 16

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Apr 16

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Mon Apr 15

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Mon Apr 15

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
The theorem of Dixmier-Malliavin and a question of Casselman
Dev Hegde, U of MN
Mon Apr 15

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Applied and Computational Mathematics Seminar

Mon Apr 15

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium

Mon Apr 15

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Apr 15

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Recent Advances in Wasserstein Distributionally Robust Optimization
Rui Gao, The University of Texas at Austin
##### Abstract:

In this talk, we consider decision-making problems under data uncertainty. In particular, we study a framework, called Wasserstein distributionally robust optimization, that aims to find a decision that hedges against a set of distributions that are close to some nominal distribution in Wasserstein metric. This framework, although being an infinite dimensional optimization, has a finite-dimensional tractable reduction in various data-driven settings by virtue of duality, and is closely related to many regularization problems in statistical learning. I will discuss the generalization error bound and asymptotic properties of such framework, and compare it with other distributional uncertainty sets including divergence-based and moment-based sets. If time permits, I will talk about an application of the framework to robust classification with limited information.

Rui Gao is an Assistant Professor of Information, Risk, and Operations Management at the McCombs School of Business at the University of Texas at Austin. He received his Ph.D. in Operations Research from Georgia Institute of Technology in 2018. His current research interests lie in the intersection of decision-making under uncertainty and statistical learning, as well as their applications in data analytics. His work has been recognized with several INFORMS prize, including finalist in Nicholson student paper competition in 2016, runner-up in the Computing Society student paper prize in 2017, and winner of the Data Mining best paper award in 2017.

Fri Apr 12

## MCFAM Seminar

5:30pm - Murphy Hall 130
Model Development & Delivery in Real World Quant Finance
Florian Huchede, Director & FX Lead Quant - CME Group
##### Abstract:

Over the last 10 years, financial companies have been increasingly using quantitative models for decision making. Well performing models can provide automatic and objective decision making as well as a certain ability to synthesize complex issues. However, models expose companies to model risk, higher development cost and longer delivery time. In this MCFAM seminar, we will cover how to reduce the model risk and time to market by using a model design process. Furthermore, we will apply the process on a particular example: OTC FX option volatility calibration.

Bio: Florian Huchedé is a Director of Quantitative Risk Management at CME Group. He leads an international team of quantitative analysts that work on designing, implementing and filing quantitative algorithms on various applications (settlement, pricing, data cleansing, risk management, product creation and large optimization). Furthermore, he is the lead quant for the FX and Equity asset classes.

Florian graduated from the Financial Mathematics program at University of Chicago (2010). He completed his undergraduate studies and MS in Engineering at Ecole Francaise dElectronique et dInformatique in Paris, France (2007). Prior to joining CME Group, he worked at Credit Agricole Asset Management Alternative Investment and at The Option Clearing Corporation.

With more than 10 years of experience, Florian is focused on innovation, creativity and giving back to the quant community. He holds three U.S. patents on risk management and financial products. Furthermore, he initiated a joint research program between University of Chicago and CME Group in 2012. Since then, the program has expanded and is being utilized by many other companies.

Fri Apr 12

## First Year Seminar

5:30pm - Vincent 364
First Year Seminar
TBA
Fri Apr 12

## Lie Theory Seminar

3:35pm - Vincent Hall 313
Lie Theory Seminar

Fri Apr 12

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Some congruences for sums of binomial coefficients
Moa Apagodu, Virginia Commonwealth University
##### Abstract:

In a recent beautiful but technical article, William Y.C. Chen, Qing-Hu Hou, and Doron Zeilberger developed an algorithm for finding and proving congruence identities (modulo primes) of indefinite sums of many combinatorial sequences, namely those (like the Catalan and Motzkin sequences) that are expressible in terms of constant terms of powers of Laurent polynomials. We first give a leisurely exposition and then extend it in two directions. The Laurent polynomials may be of several variables, and instead of single sums we have multiple sums.

Fri Apr 12

## Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri Apr 12 1:25pm - Lind 305
Stating the Obvious - Job Search to Analytics Leadership
Sandhya Surapanenii, Stratasys
##### Abstract:

From "is networking really important" to "do hiring managers read cover letters", from "why should data exploration begin with a question" to "how to build a culture of data driven decision making", we have heard it all many, many times. But these are questions that warrant a reminder. And another. And another.

I hope to be that person and remind you of a few key strategies to employ in job search and best practices to avoid pitfalls in the business world. I will share failures and lessons from my experience in data management and analytics, as well as decode marketing function.

Sandhya Surapaneni (aka Sandy) works as a Global Marketing Analytics Leader at Stratasys, a pioneer in 3D printing technology. Her current focus is on building a foundation in analytics to integrate data-driven insights into every day business decisions that align with the company's long term strategy. Prior to joining Stratasys, Sandy worked as a Database Lead at BI Worldwide, building and supporting the data layer of several web applications. Sandy has a M.S in Computer Science from the University of Texas at Arlington and a M.S in Business Analytics from Carlson School of Management. Born and raised in India, she has been a Minneapolis resident for 13 years and enjoys its lakes and coffee shops.

Fri Apr 12

9:30am -
CANCELLED

Thu Apr 11

## Special Events and Seminars

2:30pm - Vincent Hall 570
Informal Fluids Seminar with the speaker Samuel Punshon-Smith
Samuel Punshon-Smith
Thu Apr 11

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Apr 11

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Semi-Ample Asymptotic Syzygies
Juliette Bruce
##### Abstract:

I will discuss the asymptotic non-vanishing of syzygies for products of projective spaces, generalizing the monomial methods of Ein-Erman-Lazarsfeld. This provides the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.

Thu Apr 11

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Apr 11

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Thu Apr 11

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Student Number Theory Seminar

Thu Apr 11

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570
Reading Seminar on Automorphic Forms

Wed Apr 10

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Wed Apr 10

## AMS Intro to Research Seminar

5:20pm - Vincent Hall 570
AMS Intro to Research Seminar

Wed Apr 10

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Reflection functors and nilpotent endomorphisms - continuation
Dongkwan Kim, University of Minnesota
##### Abstract:

We describe how the Jordan form data of quiver representations interact with reflection functors, continuing with the paper of Garver, Patrias and Thomas: Minuscule reverse plane partitions via quiver representations.

Wed Apr 10

## PDE Seminar

3:30pm - Vincent Hall 570
Lagrangian chaos and scalar mixing in stochastic fluid mechanics
Samuel Punshon-Smith, Brown University
##### Abstract:

Lagrangian chaos refers to the chaotic behavior of
Lagrangian trajectories in a fluid. This chaotic behavior often
characterized by the dynamics having a positive Lyapunov exponent,
namely the property that initially close trajectories will separate at
an exponential rate after long time. In this talk we will consider a
variety of stochastically forced fluid models, including the 2
dimensional stochastic Navier-Stokes equations, and show that under
certain non-degeneracy conditions on the noise, the Lagrangian flow
possesses a positive Lyapunov exponent. The proof crucially uses the
theory of random dynamical systems as well as tools from Malliavin
calculus and control theory to satisfy a certain non-degeneracy
criterion originally due to Furstenberg. We will explore several
important consequences of a positive exponent for passive scalars
advected by the fluid. Most importantly, we show that these velocity
fields are almost sure exponential mixers. Specifically, using the
positive Lyapunov exponent, we obtain almost sure exponential decay in
time of passive scalars in any negative Sobolev norm through a
detailed study of ergodicity of the two point Lagrangian motion. This
work is joint with Jacob Bedrossian and Alex Blumenthal.

Wed Apr 10

## Special Events and Seminars

2:30pm - Vincent Hall 213
Arithmetic level raising for unitary groups and Beilinson-Bloch-Kato conjecture (II)
Yifeng Liu, Yale University
##### Abstract:

In this series of two talks, we will introduce the recent progress on Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives of arbitrary rank. We will discuss an important technique used in the proof, namely, the arithmetic level raising for unitary groups of even rank. We will also mention other interesting results we obtained during the course of proof. This is based on a joint work with Y. Tian, L. Xiao, W. Zhang, and X. Zhu

Tue Apr 09

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Apr 09

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Apr 09

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Tue Apr 09

## Special Events and Seminars

11:00am - Vincent Hall 213
Arithmetic level raising for unitary groups and Beilinson-Bloch-Kato conjecture (I)
Yifeng Liu, Yale University
##### Abstract:

In this series of two talks, we will introduce the recent progress on Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives of arbitrary rank. We will discuss an important technique used in the proof, namely, the arithmetic level raising for unitary groups of even rank. We will also mention other interesting results we obtained during the course of proof. This is based on a joint work with Y. Tian, L. Xiao, W. Zhang, and X. Zhu.

Mon Apr 08

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Mon Apr 08

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Classical properties of Epstein zeta functions
Adrienne Sands, University of Minnesota
Mon Apr 08

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Applied and Computational Mathematics Seminar

Mon Apr 08

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium

Mon Apr 08

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Apr 08

## IMA Data Science Lab Seminar

1:25pm - Lind 305
A Brief Overview of Quantum Computing
Vlad Pribiag, University of Minnesota, Twin Cities
##### Abstract:

Quantum computing has been receiving rapidly-growing interest from both industry and government funding agencies in the last several years. In this talk, I will provide an introduction to the key concepts of quantum mechanics as related to quantum computing, and will then outline several areas were quantum computers could make substantial contributions not accessible to classical computers. I will also provide an overview of leading approaches for developing the building blocks of future quantum computers, including work from our lab.

Fri Apr 05

## First Year Seminar

5:30pm - Vincent 364
First Year Seminar
TBA
Fri Apr 05

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Topological combinatorics of crystal posets
Molly Lynch, North Carolina State University
##### Abstract:

Crystal bases were first introduced by Kashiwara when studying modules of quantum groups. Each crystal base has an associated directed, edge colored graph called a crystal graph. In many cases, these crystal graphs give rise to a natural partial order. In this talk, we study crystal posets associated to highest weight representations. We use lexicographic discrete Morse functions to connect the Möbius function of an interval in a crystal poset with the relations that exist among crystal operators within that interval. We will discuss some further directions for this work.

Fri Apr 05

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Apr 05

## Probability Seminar

2:30pm - Vincent Hall 213
Frog model on trees with drift
Si Tang, Lehigh University
##### Abstract:

We provide a uniform upper bound on the minimal drift so that the one-per-site frog model on a d-ary tree is recurrent. To do this, we introduce a subprocess that couples across trees with different degrees. Finding couplings for frog models on nested sequences of graphs is known to be difficult. The upper bound comes from combining the coupling with a new, simpler proof that the frog model on a binary tree is recurrent when the drift is sufficiently strong. This is a joint work with E. Beckman, N. Frank, Y. Jiang, and M. Junge.

Fri Apr 05

9:30am -
CANCELLED

Thu Apr 04

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Apr 04

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Apr 04

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
An Analogue of the Hartshorne-Polini Theorem in Positive Characteristic
Zhang Wenliang, University of Illinois at Chicago
##### Abstract:

Recently, Hartshorne and Polini proved a theorem to characterize the
dimension of certain de Rham cohomology groups of a holonomic D-module
over complex numbers as the number of specific D-linear maps associated
with the holonomic D-module. In this talk, I will explain an analogue of
this result in positive characteristic for F-finite F-modules. This is a
joint work with Nicholas Switala.

Thu Apr 04

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Apr 04

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Thu Apr 04

## Student Number Theory Seminar

11:00am - Vincent Hall 213
On congruence properties of Ramanujan tau function
Dev Hegde, University of Minnesota
##### Abstract:

Serre and Swinnerton-Dyer reproved many congruence relations around 1970 for the Ramanujan tau function by reinterpreting the relations in terms of l-adic representations. We will give an introduction to this topic.

Thu Apr 04

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570
Reading Seminar on Automorphic Forms

Wed Apr 03

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Wed Apr 03

## AMS Intro to Research Seminar

5:20pm - Vincent Hall 570
AMS Intro to Research Seminar

Wed Apr 03

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Reflection functors and nilpotent endomorphisms
Dongkwan Kim, University of Minnesota
##### Abstract:

We describe how the Jordan form data of quiver representations interact with reflection functors, continuing with the paper of Garver, Patrias and Thomas: Minuscule reverse plane partitions via quiver representations.

Wed Apr 03

## PDE Seminar

3:30pm - Vincent Hall 570
Convexity of Whitham's highest cusped wavear
Bruno Vergara, Madrid
##### Abstract:

Whitham's model of shallow water waves is a non-local dispersive equation that features traveling wave solutions and also singularities. I will discuss a conjecture of Ehrnström and Wahlén on the profile of solutions of extreme form and show that there exists a highest, cusped and periodic solution convex between consecutive crests of $C^{1/2}$-regularity. The talk is based on joint work with A. Enciso and J. Gómez-Serrano.

Tue Apr 02

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Apr 02

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Apr 02

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Mon Apr 01

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Mon Apr 01

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Classical facts about Epstein zeta functions
Adrienne Sands, University of Minnesota
Mon Apr 01

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Applied and Computational Mathematics Seminar

Mon Apr 01

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Quadratic Wasserstein Metrics for Nonlinear Inverse Problems
Kui Ren, Columbia University
##### Abstract:

In the absence of analytical reconstruction methods, numerical solutions of nonlinear inverse problems have been mostly based on least-square formulations where solutions are sought by minimizing the $L^2$ difference between model predictions and measured data. We present here recent computational studies of some nonlinear inverse problems where quadratic Wasserstein distances are used to measure the discrepancy between model predictions and measured data. Related numerical and theoretical issues will be discussed.

Mon Apr 01

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Apr 01

## IMA Data Science Lab Seminar

1:25pm - Lind 305
How to Deal with Big Data? Understanding Large-scale Distributed Regression
Edgar Dobriban, Wharton School of the University of Pennsylvania
##### Abstract:

Modern massive datasets pose an enormous computational burden to practitioners. Distributed computation has emerged as a universal approach to ease the burden: Datasets are partitioned over machines, which compute locally, and communicate short messages. Distributed data also arises due to privacy reasons, such as with medical databases. It is important to study how to do statistical inference and machine learning in a distributed setting. In this talk, we present results about one-step parameter averaging in statistical linear models under data parallelism. We do linear regression on each machine, and take a weighted average of the parameters. How much do we lose compared to doing linear regression on the full data? Here we study the performance loss in estimation error, test error, and confidence interval length in high dimensions, where the number of parameters is comparable to the training data size. We discover several key phenomena. First, averaging is not optimal, and we find the exact performance loss. Second, different problems are affected differently by the distributed framework. Estimation error and confidence interval length increases a lot, while prediction error increases much less. These results match numerical simulations and a data analysis example. To derive these results, we rely on recent results from random matrix theory, where we also develop a new calculus of deterministic equivalents as a tool of broader interest.

Edgar Dobriban is an assistant professor of statistics at the Wharton School of the University of Pennsylvania. He obtained his PhD in Statistics in 2017 from Stanford University, advised by David Donoho, and his undergraduate degree in mathematics from Princeton University in 2012. His research interests are in developing statistical methods and theory for large-scale data analysis.

Fri Mar 29

## First Year Seminar

5:30pm - Vincent 364
First Year Seminar
TBA
Fri Mar 29

## MCFAM Seminar

5:30pm - Vincent Hall 16
MFM Modeling Workshop Presentations - Machine Learning in Equity Classification and Smart Beta Investing in Commodities
2019 FM Modeling Workshop Student Presentations, University of Minnesota
##### Abstract:

Two Teams of MFM students from the 2019 MFM Modeling Workshop will present their work to the Seminar. Each group will take a half hour to cover their topics, including Q & A

Machine Learning in Equity Classification: This MFM modeling workshop team worked with various machine learning classification models with the goal of classifying equities via well-known quantitative factors such as Value and Momentum. The classification was supervised, utilizing a novel ETF dataset which was supplemented extensively. The team worked in Python, especially the Scikit Learn module. They will present their project to seminar attendees

Smart Beta Investing in Commodities: Ever since the first stocks and bonds were issued by the Dutch East India Company (VOC), investors have tried to understand what drives returns. Smart Beta strategies have gained popularity lately by offering the potential for better-than-market returns with better-defined risks, especially after the recognition in 2008 that multi-asset classes can experience severe losses at the same time despite their apparent intrinsic differences. Smart beta strategies can take many different forms, with a variety of objectives. They can simply aim at reducing risks (the risk-based approach) or enhancing return through exposure to systematic factors (the factor-based approach). In commodities investing, alternative index movement was born from frustration with the inherent biases of conventional indices. For example, negative commodity roll yields can erode returns by as much as 50%. This team explored the opportunities of constructing a commodity investment portfolio that uses different smart beta approaches to seek enhancing returns and risk reduction. Factors like curve, value, and momentum were examined in the back-test.

Fri Mar 29

## Combinatorics Seminar

3:35pm - Vincent Hall 570
A combinatorial duality and the Sperner property for the weak order
Christian Gaetz, MIT
##### Abstract:

A poset is Sperner if its largest antichain is no larger than its largest rank. In the 1980's, Stanley used the Hard-Lefschetz Theorem to prove the Sperner property for strong Bruhat orders on Weyl groups. I will describe joint work with Yibo Gao in which we prove Stanley's conjecture that the weak Bruhat order on the symmetric group is also Sperner, by exhibiting a combinatorially-defined representation of sl2 respecting the structure of the weak and strong orders. I will explain how this representation gives rise to a combinatorial duality between the weak and strong Bruhat orders and leads to a strong order analogue of Macdonald's reduced word identity for Schubert polynomials.

Fri Mar 29

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Mar 29

## Probability Seminar

2:30pm - Vincent Hall 213
Moments of scores
Sergey Bobkov, UMN
##### Abstract:

If a random variable X has an absolutely continuous
density f, its score is defined to be the random variable
\rho(X) = f'(X)/f(X), where f' is the derivative of f. We will discuss
upper bounds on the moments of the scores, especially in the
case when X represents the sum of independent random variables.

Fri Mar 29 1:25pm - Lind 305
So, How Do You Get a Job?
Chang Lee, Lowe's
##### Abstract:

I was late. I only decided to find a job in industry in the 4th year of my graduate study even though I never had a job outside of academia. The one question that I kept asking was: how do you get a job?

It was scary because I did't know what to do. But I ended up getting a job. And today, I think I'm doing fine.

If you are about to start on the path to industry but you feel that you are full of questions and doubts, then this talk may be for you. In this talk, I will show you two things:

1. my experience of going into industry, and
2. how to thrive in it.

You will walk away with guidelines and tips that I learned from my mistakes and observations. It will help you save time and avoid frustrations in the process.

Chang currently works as a data scientist at Lowe's. He entered into the data science field as an intern for a baseball team, the Tampa Bay Rays. He got his Ph.D in Mathematics from Vanderbilt University in 2017 under Alex Powell. Besides math and data, Chang has become a soul food advocate and survives on barbecue and hot chicken. You can learn more about his experience outside of academia at his blog: https://changhsinlee.com and his YouTube channel: https://youtube.com/c/softwareforscience

Fri Mar 29

9:30am -
CANCELLED

Thu Mar 28

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Mar 28

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Mar 28

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Bernstein-Sato polynomials in positive characteristic and Hodge theory
Thomas Bitoun, University of Toronto
##### Abstract:

Bernstein-Sato polynomials are fundamental in D-module theory. For
example, they are the main finiteness ingredient in the construction of
nearby cycles. We will present a positive characteristic analogue of the
Bernstein-Sato polynomials. After diving in the world of characteristic
p D-modules, we shall consider how our construction varies with the
prime p. This turns out to be related to questions of Hodge theory and
Poisson homology.

Thu Mar 28

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Mar 28

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Thu Mar 28

## Student Number Theory Seminar

11:00am - Vincent Hall 213
On congruence properties of Ramanujan tau function
Dev Hegde, University of Minnesota
##### Abstract:

Serre and Swinnerton-Dyer reproved many congruence relations around 1970 for the Ramanujan tau function by reinterpreting the relations in terms of l-adic representations. We will give an introduction to this topic.

Thu Mar 28

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570
Reading Seminar on Automorphic Forms

Wed Mar 27

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Wed Mar 27

## AMS Intro to Research Seminar

5:20pm - Vincent Hall 570
AMS Intro to Research Seminar

Wed Mar 27

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Reflection functors
Dongkwan Kim, University of Minnesota
##### Abstract:

We define the notion of reflection functors between the categories of quiver representations and discuss some of their basic properties. After this, we explain how these functors are related to (generic) Jordan types and corresponding representations of quivers.

Wed Mar 27

## PDE Seminar

3:30pm - Vincent Hall 570
PDE Seminar
Luis Vega, Serrin Lecture
Tue Mar 26

## Dynamical Systems

2:30pm - Vincent Hall 313
Ice issues in conceptual climate models
Alice Nadeau, University of Minnesota
##### Abstract:

Conceptual climate models are a necessary tool for scientists trying to understand Earth and other rocky planets because they can provide insight on predominant forces affecting a planet's climate. This talk will focus on Budyko-Sellers type energy balance models, a particular class of conceptual models used to study ice-albedo feedback in the climate system. In this talk I will discuss the different ways one can represent ice in these models, including some of my recent results in extending these models to other planets.

Tue Mar 26

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Mar 26

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar
TBA
Mon Mar 25

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Mon Mar 25

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Mon Mar 25

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Low rankness in forward and inverse kinetic theory
Qin Li, University of Wisconsin
##### Abstract:

Multi-scale kinetic equations can be compressed: in certain regimes, the Boltzmann equation is asymptotically equivalent to the Euler equations, and the radiative transfer equation is asymptotically equivalent to the diffusion equation. A lot of detailed information is lost when a system passes to the limit. In linear algebra, it is equivalent to a system being of low rank. I will discuss such transition and how it affects the computation: mainly, in the forward regime, inserting low-rankness could greatly advances the computation, while in the inverse regime, the system being of low rank typically makes the problems significantly harder.

Mon Mar 25

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium

Mon Mar 25

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Mar 25

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Mark Hsiao, Netflix, Inc
Fri Mar 22

## First Year Seminar

5:30pm - Vincent 364
First Year Seminar
TBA
Fri Mar 22

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Combinatorics Seminar

Fri Mar 22

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Mar 22

## Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri Mar 22

9:30am -
CANCELLED

Thu Mar 21

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Mar 21

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Mar 21

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Commutative Algebra Seminar

Thu Mar 21

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Mar 21

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Mar 21

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Student Number Theory Seminar

Thu Mar 21

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570
Reading Seminar on Automorphic Forms

Wed Mar 20

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Wed Mar 20

## AMS Intro to Research Seminar

5:20pm - Vincent Hall 570
AMS Intro to Research Seminar

Wed Mar 20

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Algebraic Representation Theory

Tue Mar 19

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Mar 19

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Mar 19

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Mon Mar 18

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Mon Mar 18

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Mon Mar 18

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Applied and Computational Mathematics Seminar

Mon Mar 18

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium

Mon Mar 18

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri Mar 15

## First Year Seminar

5:30pm - Vincent 364
First Year Seminar
TBA
Fri Mar 15

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Cell Decompositions for Rank Two Quiver Grassmannians
Dylan Rupel, Michigan State University
##### Abstract:

A quiver Grassmannian is a variety parametrizing subrepresentations of a given quiver representation. Reineke has shown that all projective varieties can be realized as quiver Grassmannians. In this talk, I will study a class of smooth projective varieties arising as quiver Grassmannians for (truncated) preprojective representations of an n-Kronecker quiver, i.e. a quiver with two vertices and n parallel arrows between them. The main result I will present is a recursive construction of cell decompositions for these quiver Grassmannians motivated by the theory of rank two cluster algebras. If there is time I will discuss a combinatorial labeling of the cells by which their dimensions may conjecturally be directly computed. This is a report on joint work with Thorsten Weist.

Fri Mar 15

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Mar 15

## Probability Seminar

2:30pm - Vincent Hall 213
The generalized TAP free energy
Wei-Kuo Chen, UMN
##### Abstract:

Spin glasses are disordered spin systems initially invented by theoretical physicists with the aim of understanding some strange magnetic properties of certain alloys. In particular, over the past decades, the study of the Sherrington-Kirkpatrick (SK) mean-field model via the replica method has received great attention. In this talk, I will discuss another approach to studying the SK model proposed by Thouless-Anderson-Palmer (TAP). I will explain how the generalized TAP correction appears naturally and give the corresponding generalized TAP representation for the free energy. Based on a joint work with D. Panchenko and E. Subag.

Fri Mar 15

## Special Events and Seminars

2:30pm - Vincent Hall 1
Mathematical Physics, Algebraic Geometry, and Commutative Algebra
Nadia Ott
Fri Mar 15 1:25pm - Lind 305
Lecture
Karyn Sutton, The Institute for Disease Modeling
Fri Mar 15

9:30am -
CANCELLED

Thu Mar 14

## Colloquium

3:35pm - Vincent Hall 16
Short-Time Asymptotic Methods In Financial Mathematics
Jose Figueroa-Lopez, Washington University
##### Abstract:

In this talk, we will be concerned with the average values of certain random functionals of the path of a stochastic process during a given time period. High-order asymptotic characterizations of such values when the time period shrinks to 0 have a wide range of applications. In statistics, they are instrumental in establishing infill asymptotic properties of high-frequency based statistical methods of stochastic processes. In finance, they have been used as model selection and calibration tools based on near expiration option prices. In some Engineering problems, they also show up as a method to solve a problem in continuous time by looking at the analogous problem in discrete time and shrinking the time step to 0. These short-time asymptotic methods are especially useful in the study of complex models with jumps and stochastic volatility due to the lack of tractable formulas and efficient statistical and numerical procedures. In this talk, I will discuss some recent advances in the area and illustrate their broad relevance in several contexts.

Bio: Dr. Figueroa-López is a Professor in the Department of Mathematics and Statistics at Washington University in St. Louis. He currently serves as part of the executive committee and the chair of the statistics committee of the Department. Formerly he was Associate Professor of Statistics at Purdue University, where he served as Associate Director of the Computational Finance Program and as a member of the University Senate. Professor Figueroas ongoing research includes short-time asymptotics of jump-diffusion models, diffusion limits of Limit Order Book models, optimal limit order placement problems, market making via reinforced learning, and optimal tuning of high-frequency based econometric methods. He was awarded the NSF career award in 2012 and currently has two active NSF grants on the interplay of finance, statistics, and probability. He is an Associate Editor of the SIAM Journal on Financial Mathematics (SIFIN) and a former Associate Editor of Electronic Journal of Statistics.

Thu Mar 14

## Special Events and Seminars

1:25pm - Vincent Hall 113
Nearby cycles over general bases and duality
Weizhe Zheng, Chinese Academy of Sciences and Princeton University
##### Abstract:

Over one-dimensional bases, Gabber and Beilinson proved theorems on the commutation of the nearby cycle functor and the vanishing cycle functor with duality. In this talk, I will explain a way to unify the two theorems, confirming a prediction of Deligne. I will also discuss the case of higher-dimensional bases and applications to local acyclicity, following suggestions of Illusie and Gabber. This is joint work with Qing Lu.

Thu Mar 14

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Mar 14

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Towards Free Resolutions Over Scrolls
Aleksandra Sobieska-Snyder, Texas A&M
##### Abstract:

Free resolutions over the polynomial ring have a storied and active
record of study. However, resolutions over other rings are much more
mysterious; even simple examples can be infinite! In these cases, we
look to any combinatorics of the ring to glean information. This talk
will present a minimal free resolution of the ground field over the
semigroup ring arising from rational normal 2-scrolls, and (if time
permits) a computation of the Betti numbers of the ground field for all
rational normal k-scrolls.

Thu Mar 14

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Mar 14

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Mar 14

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Knots and Primes Part II: The Linking Number and Legendre Symbol
Katy Weber, University of Minnesota
##### Abstract:

We review the analogy between knots in 3-manifolds and prime ideals in number rings, and push it further to realize the Legendre symbol as the analogue of the (mod 2) linking number. This talk should be accessible even if you did knot attend seminar last week.

Thu Mar 14

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570
Reading Seminar on Automorphic Forms

Wed Mar 13

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Wed Mar 13

## AMS Intro to Research Seminar

5:20pm - Vincent Hall 570
AMS Intro to Research Seminar

Wed Mar 13

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Postponed
Dongkwan Kim, University of Minnesota
##### Abstract:

This talk is postponed to March 27.

Tue Mar 12

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Mar 12

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Mar 12

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Tue Mar 12

## Special Events and Seminars

11:00am - Vincent 213
Compatible systems along the boundary
Weizhe Zheng, Chinese Academy of Sciences and Princeton University
##### Abstract:

A theorem of Deligne says that compatible systems of l-adic sheaves on a smooth curve over a finite field are compatible along the boundary. I will present an extension of Deligne's theorem to schemes of finite type over the ring of integers of a local field. This has applications to the equicharacteristic case of some conjectures on l-independence. I will also discuss the relationship with compatible wild ramification. This is joint work with Qing Lu.

Mon Mar 11

## Representations of p-adic groups

7:30pm - Vincent Hall 213
Representations of p-adic groups

Mon Mar 11

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Mon Mar 11

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Applied and Computational Mathematics Seminar

Mon Mar 11

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium
Canceled
Mon Mar 11

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Mar 11

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Robust and Phaseless PCA (and Subspace Tracking)
Namrata Vaswani, Iowa State University
##### Abstract:

Principal Components Analysis (PCA), a.k.a. subspace learning, is one of the most widely used dimension reduction techniques that attempts to find a low-dimensional subspace approximation of a given dataset. PCA is a solved problem when the observed data is relatively clean and lies in (or close to) a low-dimensional subspace. However, in many modern applications, the data are often either incomplete (missing data) or corrupted by outliers. Robust PCA refers to this harder problem of PCA in the presence of entry-wise outliers (sparse corruptions). An important example application is video analytics when slow-changing videos are corrupted by foreground occlusions, e.g., by moving vehicles or persons. For long data sequences, e.g., long surveillance videos, if one tries to use a single subspace to represent the entire sequence, the required subspace dimension may be too large. For such data, a better model is to assume that the data subspace can change with time, albeit gradually. This problem of tracking data lying in a slowly changing subspace, while being robust to additive sparse outliers is referred to as Robust Subspace Tracking (RST). While robust PCA has received a lot of attention in the last decade, its dynamic version, RST, was largely open until recently. In a recent body of work, we have introduced the first provably correct and practically usable online solution framework for RST that we call Recursive Projected Compressive Sensing (ReProCS). Our most recent work from ICML 2018 shows that a simple ReProCS-based algorithm provides a provably fast and nearly (delay and memory) optimal RST solution under mild assumptions: weakened standard robust PCA assumptions and subspace change that is slow enough compared to the smallest magnitude outlier entry. Our theoretical claims are also backed by extensive experimental evidence for two video applications.

In new work, we have looked at what can be called the Phaseless PCA problem. This involves recovering a low-rank matrix from phaseless (magnitude-only) linear projections of each of its columns. It finds important applications in dynamic phaseless imaging applications, such as dynamic sub-diffraction imaging or Fourier ptychography, involving recovering a set of slowly-changing images that together form an approximately low-rank matrix (with each vectorized image being one column). We introduce a simple alternating minimization solution that can provable recover the low-rank matrix with sa

Fri Mar 08

## First Year Seminar

6:30pm - Vincent 364
First Year Seminar
TBA
Fri Mar 08

## MCFAM Seminar

5:30pm - Vincent Hall 16
Feb 2018 Volatility Event
Yuepeng Perry Li, CFA, FRM, Parametric Portfolio Associates LLC
##### Abstract:

On the Monday of February 5th 2018, VIX Index (measure of expected future volatility) spiked by 116% to 37.3, and massive turbulence was observed across global financial markets. During the talk, we will review this event and discuss on the following topics:

• How did we get there? --- Low volatility environment and the great snake of risk
• What happened? --- 2017s hottest trades went wrong, and several funds and firms (!) were effectively wiped out
• What did we learn?  Positioning, behavior, and never underestimate the risk of financial markets (convexity to volatility and VaR calcs)

Fri Mar 08

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Affine matrix-ball construction and its relation to representation theory
Dongkwan Kim, University of Minnesota
##### Abstract:

In 1985, Shi found a generalization of the Robinson-Schensted algorithm to (extended) affine symmetric groups and described their Kazhdan-Lusztig cells in terms of combinatorics. Recently, Chmutov, Lewis, Pylyavskyy, and Yudovina developed its generalization, called the affine matrix-ball construction (abbreviated AMBC). It provides a bijection from an (extended) affine symmetric group to the set of triples (P,Q,?) where P and Q are row-standard Young tableaux of the same shape and ? is an integer vector satisfying certain inequalities. In this talk, I will briefly explain this algorithm, and discuss how this is related to representation of (extended) affine symmetric groups, especially the asymptotic Hecke algebras introduced by Lusztig. This work is joint with Pavlo Pylyavskyy.

Fri Mar 08

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Mar 08

## Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri Mar 08 1:25pm - Lind 305
Internship/Job Searching 101: Answering Your Most Asked Beginner Questions
Whitney Moore, University of Minnesota, Twin Cities
##### Abstract:

Internship/job searching is a multifaceted process that can summon many questions along the way! During this workshop, we will aim to address your most asked questions about getting started with your search, including:
- Where to find internships/jobs to apply for
- What to look for and how to read an internship/job posting
- What you can be doing now and over the summer to help prepare for your search.
There will be time to discuss more questions during the session, so come with your questions in hand!

Whitney Moore has been a Career Counselor in the CSE Career Center at the University of Minnesota since the fall of 2011. Her passion lies in living a life of positivity and inspiring others to do the same, particularly while navigating career and leadership development. In addition to her work at the U of M, Whitney is a past President of the Minnesota College and University Career Services Association (MCUCSA) and holds degrees from Gustavus Adolphus College and Minnesota State University, Mankato. Away from campus, Whitney is motivated by running with her dog, competing in triathlon, eating baked goods, and exploring MN with her husband. As an utter positivist, you can also find her musings on living with positivity on Instagram at @ThePositivistExplorer!

Fri Mar 08

8:30am -
CANCELLED

Thu Mar 07

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Mar 07

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Mar 07

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Commutative Algebra Seminar

Thu Mar 07

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Mar 07

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Mar 07

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Knots and Primes
Eric Stucky, University of Minnesota
##### Abstract:

In this talk we will outline the basic premise for the analogy between knots (in manifolds) and primes (in number fields). This analogy involves some rather heavy definitions; we will review the topological background as needed, while taking a more intuitive angle on the arithmetic machinery. Time permitting, we will briefly sketch an extension of the Frobenius automorphism which is a major tool in understanding the analogy between the Legendre symbol and the linking number.

Thu Mar 07

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570
Reading Seminar on Automorphic Forms

Wed Mar 06

## Representations of p-adic groups

8:30pm - Vincent Hall 213
Representations of p-adic groups

Wed Mar 06

## AMS Intro to Research Seminar

6:20pm - Vincent Hall 570
AMS Intro to Research Seminar

Wed Mar 06

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Generic Jordan forms and plane partitions
Sam Hopkins, University of Minnesota
##### Abstract:

We continue the introduction of the Garver-Patrias-Thomas paper by
exploring what the map from a quiver representations to its generic Jordan
form looks like in the case of a Type A quiver, and explain how this map is
related to bijections and generating functions for plane partitions.

Wed Mar 06

## PDE Seminar

3:35pm - Vincent Hall 570
Quantitative estimates of propagation of chaos for large systems of interacting particles
Zhenfu Wang, University of Pennsylvania
##### Abstract:

We present a new method to derive quantitative estimates proving the propagation of chaos for large stochastic or deterministic systems of interacting particles. Our approach requires to prove large deviations estimates for non-continuous potentials modified by the limiting law. But it leads to explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit; and it can be applied to very singular kernels that are only in negative Sobolev spaces and include the Biot-Savart law for 2D Navier-Stokes and 2D Euler. Joint work with P.-E. Jabin.

Tue Mar 05

## Colloquium

3:35pm - Vincent Hall 16
Cohomology of Shimura varieties
Sug Woo Shin, U.C. Berkeley
##### Abstract:

Shimura varieties are a certain class of algebraic varieties over number fields with lots of symmetries, introduced by Shimura and Deligne nearly half a century ago. They have been playing a central role in number theory and other areas. Langlands proposed a program to compute the L-functions and cohomology of Shimura varieites in 1970s; this was refined by Langlands-Rapoport and Kottwitz in 1980s. I will review some old and recent results in this direction.

Tue Mar 05

## Dynamical Systems

2:30pm - Vincent Hall 313
Measuring attractor strength using bounded, nonautonomous control
Kate Meyer, UMN
##### Abstract:

A topological definition of an attractor leaves out metric information relevant to modeling real-world systems, particularly how far the attractor persists against perturbations and error. This talk will review some existing approaches to measuring the strength of an attractor in metric terms and will introduce the quantity intensity to generalize basin steepness to systems of autonomous ODEs in arbitrary dimension. One can compute an attractors intensity by probing a domain of attraction with bounded, non-autonomous control and tracking the sets reachable from the attractor. A connection between reachable sets and isolating blocks implies that an attractors intensity not only reflects its capacity to retain solutions under time-varying perturbations, but also gives a lower bound on the distance the attractor continues in the space of vector fields.
?

Tue Mar 05

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Mar 05

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Mon Mar 04

## Representations of p-adic groups

8:30pm - Vincent Hall 213
Representations of p-adic groups

Mon Mar 04

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory

Mon Mar 04

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Applied and Computational Mathematics Seminar

Mon Mar 04

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium

Mon Mar 04

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Mar 04

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Peculiar Properties of Locally Linear Embedding -- Toward Theoretical Understanding of Unsupervised Learning
Hau-tieng Wu, Duke University
##### Abstract:

Since its introduction in 2000, the locally linear embedding (LLE) has been widely applied as an unsupervised learning tool. However, only few hand-waiving arguments are available to explain what is going on before 2018. For the sake of scientific soundness, we provide a systematic analysis of LLE, particularly under the manifold setup. In this talk, several theoretical results will be discussed. (1) We derive the corresponding kernel function, which in general is asymmetric and and not form a Markov process. (2) The regularization is critical. Different regularizations lead to dramatically different results. If chosen correctly, asymptotically we obtain the Laplace-Beltrami operator even under nonuniform sampling. (3) It has an intimate relationship with the local covariance analysis and tangent bundle structure. (4) When the boundary is not empty, we run into an interesting mixed-type differential equation. (5) An ingredient of the kernel provides a novel way to detect boundary, and hence a new approach to derive the Laplace-Beltrami operator with the Dirichlet boundary condition. If time permits, its relationship with several statistical topics like the locally linear regression and error in variable will be discussed. This is a joint work with Nan Wu.

Fri Mar 01

## First Year Seminar

6:30pm - Vincent 364
First Year Seminar
TBA
Fri Mar 01

## MCFAM Seminar

5:30pm - Vincent Hall 16
Introduction to model selection principles for data analysis in the era of Big Data
Jie Ding, School of Statistics - University of Minnesota
##### Abstract:

In the era of big data, analysts usually explore various statistical models or machine learning methods for observed data in order to facilitate scientific discoveries or gain predictive power. Whatever data and fitting procedures are employed, a crucial step is to select the most appropriate model or method from a set of candidates. Model selection is a key ingredient in data analysis for reliable and reproducible statistical inference or prediction, and thus central to scientific studies in fields such as ecology, economics, engineering, finance, political science, biology, and epidemiology. There has been a long history of model selection techniques that arise from researches in statistics, information theory, and signal processing. A considerable number of methods have been proposed, following different philosophies and exhibiting varying performances. The purpose of this talk is to bring an overview of them, in terms of their motivation, large sample performance, and applicability. I will provide practically relevant discussions on theoretical properties of state-of- the-art model selection approaches, and share some thoughts on controversial views on the practice of model selection.

Fri Mar 01

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Quotients of symmetric polynomial rings deforming the cohomology of the Grassmannian
Darij Grinberg
##### Abstract:

One of the many connections between Grassmannians and combinatorics is cohomological: The cohomology ring of a Grassmannian Gr(k,n) is a quotient of the ring S of symmetric polynomials in k variables. More precisely, it is the quotient of S by the ideal generated by the k consecutive complete homogeneous symmetric polynomials hn?k+1,hn?k+2,...,hn. We propose and begin to study a deformation of this quotient, in which the ideal is instead generated by hn?k+1?a1,hn?k+2?a2,...,hn?ak for some k fixed elements a1,a2,...,ak of the base ring. This generalizes both the classical and the quantum cohomology rings of Gr(k,n). We find two bases for the new quotient, as well as an S3-symmetry of its structure constants, a "rim hook rule" for straightening arbitrary Schur polynomials, and a fairly complicated Pieri rule. We conjecture that the structure constants are nonnegative in an appropriate sense (treating the ai as signed indeterminate), which suggests a geometric or combinatorial meaning for the quotient. There are multiple open questions and opportunities for further research.

Fri Mar 01

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Mar 01

## Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri Mar 01 1:25pm - Lind 305
Lecture
Sohan Das, EVS, Inc.
Fri Mar 01

8:30am -
CANCELLED

Thu Feb 28

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Feb 28

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Feb 28

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Virtual Resolutions of Monomial Ideals
Jay Yang, University of Minnesota
##### Abstract:

Virtual resolutions as defined by Berkesch, Erman, and Smith,
provide a more geometrically meaningful generalization of free
resolutions in the case of subvarieties of a toric variety. In this
setting I prove an analog of Hilbert's syzygy theorem for virtual
resolutions of monomial ideals in toric varieties subject to some mild
conditions.

Thu Feb 28

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Feb 28

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Feb 28

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Finite Hecke Algebras and Their Characters
Andy Hardt, University of Minnesota
##### Abstract:

We explore some of the major results in the study of finite Hecke algebras and their character tables. These algebras are useful in the study of representations of finite Chevalley groups, and also appear in the study of quantum groups and knot/link invariants. We'll run through some equivalent definitions of this versatile object, and then talk about a couple approaches to its character theory. In particular, Starkey's rule is a combinatorial formula for the character table of the type A finite Hecke algebra. We'll briefly sketch a proof of this result and talk about the possibility for extension to other types. Starkey's rule allows us to calculate the weights of Ocneanu traces, which are important invariants in knot theory relating to type A Hecke algebras, and a type B version of Starkey's rule would give us insights into the type B analogue to Ocneanu traces.

Thu Feb 28

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570
Reading Seminar on Automorphic Forms

Wed Feb 27

## Representations of p-adic groups

8:30pm - Vincent Hall 213
Representations of p-adic groups

Wed Feb 27

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Jordan form data of quiver representations
Sam Hopkins, University of Minnesota
##### Abstract:

We introduce the paper of Garver, Patrias and Thomas: Minuscule reverse plane partitions via quiver representations, starting with a review of aspects of quiver representations.

Wed Feb 27

## AMS Intro to Research Seminar

12:20pm - Vincent Hall 570
AMS Intro to Research Seminar
Adrienne Sands
Tue Feb 26

## Dynamical Systems

2:30pm - Vincent Hall 313
Spectral Consequences of Hidden Symmetry in Network Dynamical Systems
Eddie Nijholt, UIUC
##### Abstract:

Network dynamical systems play an important role in many fields of science; whenever there are agents whose time evolution is linked through some interaction structure, we may view the system as a network and model it accordingly. However, despite their prevalence, network dynamical systems are in general not well understood. One can identify two reasons for this. First of all, many coordinate changes and other transformations from well-known dynamical systems techniques do not respect the underlying network structure. Second of all, despite this somewhat ethereal' character, systems with a network structure often display behavior that is highly anomalous for general dynamical systems. Examples of this include very unusual bifurcation scenarios and high spectral degeneracies. As a possible explanation of this, it can be shown that a large class of network ODEs admit hidden symmetry, which may be discovered through the so-called fundamental network construction. In most cases, this underlying symmetry does not come from a group though, but rather from a more general algebraic structure such as a monoid or category. I will show how the fundamental network allows one to adapt techniques from dynamical systems theory to a network setting, and how some of the more unusual properties of networks may be explained. In doing so, I will mostly focus on spectral properties of linear network maps.
?

Tue Feb 26

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Feb 26

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Mon Feb 25

## Representations of p-adic groups

8:30pm - Vincent Hall 213
Representations of p-adic groups

Mon Feb 25

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Integral representations and meromorphic continuations of Eisenstein series and L-functions
Paul Garrett, University of Minnesota
Mon Feb 25

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Primal dual methods for Wasserstein gradient flows
Li Wang, University of Minnesota
##### Abstract:

We develop a variational method for nonlinear equations with a gradient flow structure. Such equations arise in applications of a wide range, such as porous median flows, material science, animal swarms, and chemotaxis. Our method builds on the JKO framework, which evolves the equation as a gradient flow with respect to the Wasserstein metric. As a result, our method has built-in positivity preserving, entropy decreasing properties, and overcomes stability issue due to the strong nonlinearity and degeneracy. Furthermore, our method is massively parallelizable, and thus extremely efficient in high dimensions. Upon discretization of the PDE constraint, we also prove the ??convergence of the fully discrete optimization towards the continuum JKO scheme.

Mon Feb 25

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium

Mon Feb 25

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Feb 25

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Strong Coresets for k-Median and Subspace Approximation: Goodbye Dimension
David Woodruff, Carnegie Mellon University
##### Abstract:

We obtain the first strong coresets for the k-median and subspace approximation problems with sum of distances objective function, on n points in d dimensions, with a number of weighted points that is independent of both n and d; namely our coresets have size poly(k/eps). A strong coreset (1+eps)-approximates the cost function for all possible sets of centers simultaneously. We also give input sparsity time algorithms for computing these coresets, which are fixed parameter tractable in k/eps. We obtain the result by introducing a new dimensionality reduction technique for coresets that significantly generalizes earlier results for squared Euclidean distances to sums of p-th powers of Euclidean distances for constant p >= 1.

Joint work with Christian Sohler

Fri Feb 22

## First Year Seminar

6:30pm - Vincent 364
First Year Seminar
TBA
Fri Feb 22

## MCFAM Seminar

5:30pm - Vincent Hall 112
The Prospect of a Forgivable Premium Insurance Policy
Kyle Jore, University of Minnesota
##### Abstract:

Despite low premiums and high subsidies, farmers view crop insurance programs as a gamble. One explanation, in a revenue protection program, is that farmers exhibit loss aversion when premiums are just above coverage. Introducing a model for conditional loss aversion (CLA), in the context of cumulative prospect theory, it can be shown that the introduction of a forgivable premium can remove the producers loss aversion. This would result in producers being willing to spend more on an insurance program and thus, allow for a reduction in the implied subsidy.

Fri Feb 22

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Counting factorizations in complex reflection groups
Joel Lewis, George Washington University
##### Abstract:

In this talk, I'll discuss ongoing work with Alejandro Morales generalizing a 30-year old result of Jackson on permutation enumeration: we consider the enumeration of arbitrary factorizations of a Coxeter element in a well generated finite complex reflection group, keeping track of the fixed space dimension of the factors. As in the case of the symmetric group, the factorization counts are ugly, so the goal is to choose a basis for the generating function in which the answer is nice. In the case of the infinite families of monomial matrices, we accomplish this via combinatorial arguments; a notion of transitivity of a factorization appears for the "type D" group G(m, m, n). I'll also describe some puzzling partial results in the exceptional cases.

Fri Feb 22

## PDE Seminar

3:35pm - Vincent Hall 311
Special PDE Seminar - How to obtain parabolic theorems from their elliptic counterparts
Blair Davey, City College of New York
##### Abstract:

Experts have long realized the parallels between elliptic and parabolic theory of partial differential equations. It is well-known that elliptic theory may be considered a static, or steady-state, version of parabolic theory. And in particular, if a parabolic estimate holds, then by eliminating the time parameter, one immediately arrives at the underlying elliptic statement. Producing a parabolic statement from an elliptic statement is not as straightforward. In this talk, we demonstrate a method for producing parabolic theorems from their elliptic analogs. Specifically, we show that an $L^2$ Carleman estimate for the heat operator may be obtained by taking a high-dimensional limit of $L^2$ Carleman estimates for the Laplacian. Other applications of this technique will be discussed.

Fri Feb 22

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Feb 22

## Probability Seminar

2:30pm - Vincent Hall 213
Largest Entries of Sample Correlation Matrices from Equi-correlated Normal Populations
Tiefeng Jiang, UMN
##### Abstract:

We the limiting distribution of the largest off-diagonal entry of the sample correlation matrices of high-dimensional Gaussian populations with equi-correlation structure. Assume the entries of the population distribution have a common correlation coefficient r >0 and both the population dimension p and the sample size n tend to infinity with log p=o(n^{1/3}).
As 0< r<1, we prove that the largest off-diagonal entry of the sample correlation matrix converges to a Gaussian distribution, and the same is true for the sample covariance matrix as 0< r<1/2. This differs substantially from a well-known result for the independent case where r=0, in which the above limiting distribution is an extreme-value distribution. We then study the phase transition between these two limiting distributions and identify the regime of r where the transition occurs. It turns out that the thresholds of such a regime depend on n and converge to zero. If r is less than the threshold, larger than the threshold or is equal to the threshold, the corresponding limiting distribution is the extreme-value distribution, the Gaussian distribution and a convolution of the two distributions, respectively. The proofs rely on a subtle use of the Chen-Stein Poisson approximation method, conditioning, a coupling to create independence and a special property of sample correlation matrices. The results are then applied to evaluating the power of a high-dimensional testing problem of identity correlation matrix.

Fri Feb 22 1:25pm - Lind 305
Industrial Problems in Digital Retail
Samantha Schumacher, Target Corporation
##### Abstract:

Target is rapidly growing into the online retail space. Behind that growth, there are a lot of advanced mathematical problems to solve. Some mathematics problems in supply chain are easy to spot (traveling salesman problem!), and some are less obvious. Well talk through at least 2 less-obvious problems which are currently being investigated by Targets Supply Chain analytics teams. The goal of this talk is to give insight into the broad range of problems we are solving at Target. Additionally, Ill spend a little time talking about solutions. What makes a good solution in Industry? What makes a good problem?

Samantha Schumacher has been working math problems at Target for the last 5 years. She currently leads an analytics and engineering team for the network planning & digital fulfillment of Targets supply chain. She has her PhD in applied mathematics from University of Minnesota and an undergraduate degree in theater from Smith College. So, if all goes according to plan, she will use those theater skills to keep the talk engaging! She is also the long-time author of the blog: www.SocialMathematics.net which considers the interaction of mathematics and the modern world.

Fri Feb 22

8:30am -
CANCELLED

Thu Feb 21

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Feb 21

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Feb 21

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Commutative Algebra Seminar

Thu Feb 21

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Feb 21

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Feb 21

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Student Number Theory Seminar - Cancelled

Thu Feb 21

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570
Reading Seminar on Automorphic Forms

Wed Feb 20

## Representations of p-adic groups

8:30pm - Vincent Hall 213
Representations of p-adic groups
TBD
Wed Feb 20

## AMS Intro to Research Seminar

6:20pm - Vincent Hall 570
AMS Intro to Research Seminar

Wed Feb 20

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Semisimplicity of Deligne's category Rep(S_t)
Peter Webb, University of Minnesota
##### Abstract:

Continuing to follow the paper of Comes and Ostrik, On blocks of Deligne's category Rep(S_t), we prove the result in Section 3 that the category is semisimple except for countably. many values of t. The proof is an interesting use of the characterization of semisimple algebras by non-degeneracy of the trace form.

Tue Feb 19

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Feb 19

## Math Physics Seminar

12:20pm - Vincent Hall 209
Invariants of Finite and Discrete Group Actions Via Moving Frames
Peter Olver
##### Abstract:

The equivariant moving frame method is adapted to algorithmically construct complete, minimal sets of generating invariants for finite or, more generally, discrete group actions, both linear and nonlinear. The resulting invariants are piecewise analytic and admit a rewrite rule that allows one to immediately express any other invariant (polynomial, rational, smooth, analytic, etc.) as a function of the generating invariants. The talk will be elementary and no a priori knowledge of invariant theory or moving frames will be assumed.

Tue Feb 19

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Mon Feb 18

## Representations of p-adic groups

8:30pm - Vincent Hall 213
Representations of p-adic groups

Mon Feb 18

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Integral Representations
Paul Garrett, University of Minnesota
Mon Feb 18

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 113
Nonperturbative nonlinear effects in the dispersion relations for TE and TM plasmons on two-dimensional materials
Vera Andreeva
##### Abstract:

We analytically obtain the dispersion relations for transverse-electric (TE) and transverse-magnetic (TM) surface plasmon-polaritons in a nonlinear two-dimensional (2D) conducting material with inversion symmetry lying between two Kerr-type dielectric media. To this end, we use Maxwell's equations within the quasielectrostatic, weakly dissipative regime. We show that the wavelength and propagation distance of surface plasmons decrease due to the nonlinearity of the surrounding dielectric. In contrast, the effect of the nonlinearity of the 2D material depends on the signs of the real and imaginary parts of the third-order conductivity. Notably, the dispersion relations obtained by naively replacing the permittivity of the dielectric medium by its nonlinear counterpart in the respective dispersion relations of the linear regime are not accurate. We apply our analysis to the case of doped graphene and make predictions for the surface plasmon wavelength and propagation distance.

Mon Feb 18

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 313
Applied and Computational Math Colloquium

Mon Feb 18

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri Feb 15

## First Year Seminar

6:30pm - Vincent 364
First Year Seminar
TBA
Fri Feb 15

## MCFAM Seminar

5:30pm - Vincent Hall 16
Simulating the Greeks of American Options
P.A. (Phuong Anh) Nguyen, University of Minnesota
##### Abstract:

Abstract: In this paper, we implement an efficient simulation-based method for estimating the Greeks of American options. We perform a least square regression to determine the optimal stopping rule that is applied to calculate the Greeks, which are derived via a path-wise derivative approach. We prove that this method provides asymptotically unbiased simulation estimators for the Greeks. In addition, we propose a boundary integral technique as a faster way to approximate gamma. This technique can also be used to calculate delta and theta. Our paper is the first to provide complete simulation-based approximations for all of the Greeks (delta, gamma, theta, rho, and vega) of American options. To make the computational process more efficient, we incorporate a Brownian Bridge into the numerical simulations. We then extend the application to American basket options.

Bio: P.A. Nguyen is a PhD candidate in the University of Minnesota's Industrial Systems Engineering (ISyE) Doctoral Program. She is working with Dr. Dan Mitchell whose focus is in the area of financial engineering, specifically applying stochastic control to problems in finance and quantitative risk management. P.A. is also an alumna of the Master of Financial Mathematics (MFM) at the University of Minnesota (2014) and is currently a teaching assistant for the MFM. She worked in enterprise risk management, primarily in credit risk and interest rate risk areas, for a few years before joining UMNs ISyE PhD program.

Fri Feb 15

## Lie Theory Seminar

3:35pm - Vincent Hall 313
Lie Theory Seminar
Lue Pan,, University of Chicago
Fri Feb 15

## Special Events and Seminars

3:35pm - Vincent Hall 313
Fontaine-Mazur conjecture in the residually reducible case (II)
Lue Pan, University of Chicago
##### Abstract:

We prove the modularity of some two-dimensional residually reducible p-adic Galois representations over Q when p is at least 5. In the first talk, I will present a generalization of Emerton's local-global compatibility result. In the second talk, I will use this compatibility result to make a patching argument for completed homology in this setting.

Fri Feb 15

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Plabic R-Matrices
Sunita Chepuri, University of Minnesoa
##### Abstract:

Postnikov's plabic graphs in a disk are used to parametrize totally positive Grassmannians. One of the key features of this theory is that if a plabic graph is reduced, the face weights can be uniquely recovered from boundary measurements. On surfaces more complicated than a disk this property is lost. In this talk, we investigate a certain semi-local transformation of weights for plabic networks on a cylinder that preserves boundary measurements. We call this a plabic R-matrix. We explore the properties of the plabic R-matrix, including the symmetric group action it induces on plabic networks and its underlying cluster algebra structure.

Fri Feb 15

## Probability Seminar

2:30pm - Vincent Hall 213
Probability Seminar

Fri Feb 15

8:30am -
CANCELLED

Thu Feb 14

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Feb 14

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Feb 14

## Special Events and Seminars

1:25pm - Vincent Hall 113
Fontaine-Mazur conjecture in the residually reducible case (I)
Lue Pan, University of Chicago
##### Abstract:

We prove the modularity of some two-dimensional residually reducible p-adic Galois representations over Q when p is at least 5. In the first talk, I will present a generalization of Emerton's local-global compatibility result. In the second talk, I will use this compatibility result to make a patching argument for completed homology in this setting.

Thu Feb 14

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Commutative Algebra Seminar

Thu Feb 14

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Feb 14

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Feb 14

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Counting Number Fields, Second Order Asymptotics, and Hurwitz Spaces
Greg Michel, University of Minnesota
##### Abstract:

I'll introduce well-known counting conjectures related to number fields of bounded discriminants, and then I'll talk about some semi-related topological ideas that may allow us to strengthen these conjectures in certain situations.

Thu Feb 14

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570
Reading Seminar on Automorphic Forms

Wed Feb 13

## Representations of p-adic groups

8:30pm - Vincent Hall 213
Representations of p-adic groups
TBD
Wed Feb 13

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Indecomposable objects in Deligne's category Rep(S_t) - continuation
Peter Webb, University of Minnesota
##### Abstract:

We continue with Section 3 of the paper by Comes and Ostrik, On blocks of Deligne's category Rep(S_t). Section 3 begins with the result that the indecomposable objects are parametrized by partitions of all sizes, and this has to do with a description of the idempotents in the partition algebras. We use a fundamental relationship that goes back to Green, between idempotents an algebra, and idempotents in a factor algebra by an idempotent, and in the algebra obtained by cutting by that idempotent.

Wed Feb 13

## AMS Intro to Research Seminar

12:20pm - Vincent Hall 570
1st Annual AMS Sock Derangement
TBA
##### Abstract:

In combinatorics there is a classic problem about a "hat check," where patrons submit their hats, return slips are lost, and people get them back willy nilly. People get sad, angry, happy, you name it! In fact, as the number of people checking hats goes to infinity, the probability that NO ONE gets their hat back goes to 1/e! Well, here at the U of M math department, we are all about generalizations. Therefore, we present to you: The 1st annual AMS Sock Derangement! (a generalization of the AMS hat check)

Tue Feb 12

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Feb 12

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Feb 12

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Tue Feb 12

## PDE Seminar

10:00am - Vincent Hall 570
Global existence in incompressible fluid equations
Javier Gomez-Serrano, Princeton University
##### Abstract:

There has been high scientific interest to understand the behavior of the surface quasi-geostrophic (SQG) equation because it is a possible model to explain the formation of fronts of hot and cold air and because it also exhibits analogies with the 3D incompressible Euler equations. It is not known at this moment if this equation can produce singularities or if solutions exist globally. In this talk, I will discuss some recent works on the existence of global solutions for the SQG and modified SQG equations.

Mon Feb 11

## MCFAM Distinguished Lecture Series

5:30pm - Vincent Hall 16
Coding Capital: The Legal vs. The Digital Code
Katharina Pistor, Columbia Law School
##### Abstract:

In my forthcoming book, The Code of Capital: How Law Creates Wealth and Inequality, I argue that capital is coded in law, or more specifically in core institutions of private law, including property, collateral, trust, corporate, bankruptcy as well as contract law. These modules of the code of capital bestow critical attributes on simple assets, such as objects or claims, and there by transform them from simple into a wealth generating assets. These attributes are priority, durability, convertibility and universality, and critically, they depend on effective state backing. Recently, law has met a potential competitor in the form of the digital code. Blockchain and similar technologies, in particular, makes it possible to encode commitments such that they will be executed irrespective of a change of heart, or circumstances. Decentralized verification of resources and rights instead of ex post vindication of legal title promises a world without courts and without coercive law enforcement. In short, a new code may be on the horizon and its relation to the legacy, or legal, code raises fundamental questions about how to organize economic relations in an uncertain world and about who gets to set the parameters for doing so.

Bio: Katharina Pistor is the Edwin B. Parker Professor of Comparative Law at Columbia Law School and director of the Law Schools Center on Global Legal Transformation. Her research and teaching spans corporate law, corporate governance, money and finance, property rights, comparative law and law and development. She has published widely in legal and interdisciplinary journals and is the author can co-author of several books. She is the recipient of the Max Planck Research Award (2012) and of several grants by, among others the Institute for New Economic Thinking, and the National Science Foundation. Her most recent book, The Code of Capital: How the Law Creates Wealth and Inequality is forthcoming at Princeton University Press.

Mon Feb 11

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Integral representations of cuspidal-data Eisenstein series
Paul Garrett, University of Minnesota
Mon Feb 11

## PDE Seminar

3:35pm - Vincent Hall 313
Computer-Assisted Proofs in Partial Differential Equations
Javier Gomez-Serrano, Princeton University
##### Abstract:

In the last 50 years computing power has experienced an enormous development: every two years the number of transistors has doubled since the 1970s. However, even nowadays when we can perform very fast computations it is not clear a priori if one can obtain rigorous results based on the output of computer calculations. In this talk I will explain the basics of interval analysis and how it can be used to prove theorems in different contexts of PDE, ranging from fluid dynamics to spectral geometry.

Mon Feb 11

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Feb 11

## Applied and Computational Mathematics Seminar

3:30pm - Vincent Hall 113
Applied and Computational Mathematics Seminar
Vera Andreeva rescheduled - February 18
Mon Feb 11

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Greg Shakhnarovich, Toyota Technological Institute at Chicago
Fri Feb 08

## First Year Seminar

6:30pm - Vincent 364
First Year Seminar
TBA
Fri Feb 08

## MCFAM Seminar

5:30pm - Vincent Hall 16
Today's Seminar - Canceled
Jie Ding, School of Statistics - University of Minnesota
##### Abstract:

In the era of big data, analysts usually explore various statistical models or machine learning methods for observed data in order to facilitate scientific discoveries or gain predictive power. Whatever data and fitting procedures are employed, a crucial step is to select the most appropriate model or method from a set of candidates. Model selection is a key ingredient in data analysis for reliable and reproducible statistical inference or prediction, and thus central to scientific studies in fields such as ecology, economics, engineering, finance, political science, biology, and epidemiology. There has been a long history of model selection techniques that arise from researches in statistics, information theory, and signal processing. A considerable number of methods have been proposed, following different philosophies and exhibiting varying performances. The purpose of this talk is to bring an overview of them, in terms of their motivation, large sample performance, and applicability. I will provide practically relevant discussions on theoretical properties of state-of- the-art model selection approaches, and share some thoughts on controversial views on the practice of model selection.

Fri Feb 08

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Whitney Numbers for Cones
Galen Dorpalen-Barry, University of Minnesota
##### Abstract:

An arrangement of hyperplanes dissects space into connected components called chambers. A nonempty intersection of halfspaces from the arrangement will be called a cone. The number of chambers of the arrangement lying within the cone is counted by a theorem of Zaslavsky, as a sum of certain nonnegative integers that we will call the cone's "Whitney numbers of the 1st kind". For cones inside the reflection arrangement of type A (the braid arrangement), cones correspond to posets, chambers in the cone correspond to linear extensions of the poset, and these Whitney numbers refine the number of linear extensions. We present some basic facts about these Whitney numbers, and interpret them for two families of poset

Fri Feb 08

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Feb 08

## Probability Seminar

2:30pm - Vincent Hall 213
Stability of the Bakry-Emery theorem on R^n
Tom Courtade, UC Berkeley
##### Abstract:

In R^n, the Bakry-Émery theorem states that the sharp constant in various functional inequalities for uniformly log-concave measures is no worse than the sharp constant for the Gaussian measure. As a consequence, uniformly log-concave measures inherit certain nice features of the Gaussian, like good measure concentration properties.

In this talk, I'll discuss quantitative stability estimates for the Bakry-Émery bound on logarithmic Sobolev and Poincaré constants. In particular, if a 1-uniformly log-concave measure has almost the same logarithmic Sobolev or Poincaré constant as the standard Gaussian measure, then it must (almost) split off a Gaussian factor. As a corollary, we obtain dimension-free stability estimates for Gaussian concentration of Lipschitz functions. The proofs combine Steins method, optimal transport, and simple variational arguments.

Joint work with Max Fathi.

Fri Feb 08

## IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Lecture
Karyn Sutton, The Institute for Disease Modeling
Fri Feb 08

8:30am -
CANCELLED

Thu Feb 07

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Feb 07

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Feb 07

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Commutative Algebra Seminar

Thu Feb 07

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Feb 07

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Feb 07

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Student Number Theory Seminar

Thu Feb 07

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570
Reading Seminar on Automorphic Forms

Wed Feb 06

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Indecomposable objects in Deligne's category Rep(S_t)
Peter Webb, University of Minnesota
##### Abstract:

We will start on Section 3 of the paper by Comes and Ostrik, On blocks of Deligne's category Rep(S_t). This will be preceded by a review of the set-up in this category, which is built up out of partition algebras. Section 3 begins with the result that the indecomposable objects are parametrized by partitions of all sizes.

Tue Feb 05

## Colloquium

3:35pm - Vincent Hall 16
A Multiscale/Multiphysics Coupling Framework for Heart Valve Damage
Yue Yu, Lehigh University
##### Abstract:

Bioprosthetic heart valves (BHVs) are the most popular artificial replacements for diseased valves that mimic the structure of native valves. However, the life span of BHVs remains limited to 10-15 years, and the mechanisms that underlie BHVs failure remain poorly understood. Therefore, developing a unifying mathematical framework which captures material damage phenomena in the fluid-structure interaction environment would be extremely valuable for studying BHVs failure. Specifically, in this framework the computational domain is composed of three subregions: the fluid (blood) , the fracture structure (damaged BHVs) modeled by the recently developed nonlocal (peridynamics) theory, and the undamaged thin structure (undamaged BHVs). These three subregions are numerically coupled to each other with proper interface boundary conditions.

In this talk, I will introduce two sub-problems and the corresponding numerical methods we have developed for this multiscale/multiphysics framework. In the first problem the coupling strategy for fluid and thin structure is investigated. This problem presents unique challenge due to the large deformation of BHV leaflets, which causes dramatic changes in the fluid subdomain geometry and difficulties on the traditional conforming coupling methods. To overcome the challenge, the immersogeometric method was developed where the fluid and thin structure are discretized separately and coupled through penalty forces. To ensure the capability of the developed method in modeling BHVs, we have verified and validated this method. The second problem focuses on the nonlocal Neumann-type interface boundary condition which plays a critical role in the fluidperidynamics coupling framework. In the nonlocal models the Neumann-type boundary conditions should be defined in a nonlocal way, namely, on a region with non-zero volume outside the surface, while in fluidstructure interfaces the hydrodynamic loadings from the fluid side are typically provided on a sharp co-dimensional one surface. To overcome this challenge, we have proposed a new nonlocal Neumann-type boundary condition which provides an approximation of physical boundary conditions on a sharp surface, with an optimal asymptotic convergence rate to the local counter part. Based on this new boundary condition, we have developed a fluidperidynamics coupling framework without overlapping regions.

Tue Feb 05

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Feb 05

## Math Physics Seminar

12:20pm - Vincent Hall 209
Choreography in 3-body Classical Mechanics
Sasha Turbiner, ICN-UNAM, Mexico
##### Abstract:

By definition the choreography (dancing curve) is the trajectory
on which n classical bodies move chasing each other without collisions
with equal time delay. The first choreography (the remarkable Figure Eight)
at zero angular momentum was discovered unexpectedly by C Moore
(Santa Fe Institute) in 1993 for 3 equal masses in R^3 Newtonian gravity, numerically
and rigorously confirmed by Chenciner-Montgomery (2000). At the moment
about 6,000 choreographies are known, all numerically, in Newtonian gravity.
Possibly all known dancing curves are non-algebraic.

Does there exist (non)-Newtonian gravity for which the dancing curve is known
analytically? - Yes, a single example is known - it is the algebraic
lemniscate by Jacob Bernoulli (1694) - and it will be a concrete subject of the talk. Astonishingly, Newtonian Figure Eight coincides with algebraic lemniscate with
\chi^2 deviation 10^{-7}. Both choreographies admit any odd numbers of bodies
on them. 3-body choreography on algebraic lemniscate defines maximally
superintegrable trajectory with seven constants of motion and, possible,
polynomial algebra of integrals.

Tue Feb 05

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Mon Feb 04

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory
Postponed
Mon Feb 04

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Feb 04

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Tom Needham, The Ohio State University
Fri Feb 01

## First Year Seminar

6:30pm - Vincent 364
First Year Seminar
TBA
Fri Feb 01

## MCFAM Seminar

5:30pm - Vincent Hall 16
Computational Issues in Making Math Models Operational in Insurance
Scott Monitor, VP & Financial Engineer - MFM alumnus, FSA
##### Abstract:

Many insurance companies offer a wide array of investment guarantees, and some of these are complicated and have no clear analytical solution. In order to manage these contracts and along with increased scrutiny from regulatory bodies, companies are having to value these contracts more frequently and in a greater number of runs. We will demonstrate methodologies and computational approaches to be able to perform analysis on these contract that can be actionable and timely.

Fri Feb 01

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Enumerating Linear Systems on Graphs
David Perkinson, Reed College
##### Abstract:

To play the dollar game on a graph, start by assigning to each vertex a number of dollars of either wealth or debt. From this initial state, called a "divisor", the vertices lend and borrow with their neighbors according to chip-firing rules in an attempt to reach a debt-free state. The set of all possible winning states is the "complete linear system" of the divisor. We are interested in determining its cardinality. In the figure below, each vertex represents one of the 201 winning positions resulting from giving ten dollars to one vertex of the cycle graph on five vertices. This is joint work with Sarah Brauner and Forrest Glebe.

Fri Feb 01

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Feb 01

## Probability Seminar

2:30pm - Vincent Hall 213
Nonequilibrium particle systems in inhomogeneous space
Leonid Petrov, University of Virginia
##### Abstract:

I will discuss stochastic interacting particle systems in the Kardar-Parisi-Zhang universality class evolving in one-dimensional inhomogeneous space. The inhomogeneity means that the speed of a particle depends on its location. I will focus on integrable cases, i.e., for which certain observables can be written in an exact form suitable for asymptotic analysis. Examples include a new continuous-space version of TASEP (totally asymmetric simple exclusion process), and the pushTASEP (=long-range TASEP). For integrable systems, limit shapes of particles density can be described in an explicit way. Asymptotics of fluctuations around infinite traffic jams, also available explicitly, bring phase transitions of a novel nature.

Fri Feb 01

8:30am -
CANCELLED

Thu Jan 31

## Colloquium

3:35pm - Vincent Hall 16
From infinite random matrices over finite fields to square ice
Leonid Petrov, University of Virginia
##### Abstract:

Asymptotic representation theory of symmetric groups is a rich and beautiful subject with deep connections with probability, mathematical physics, and algebraic combinatorics. A one-parameter deformation of this theory related to infinite random matrices over a finite field leads to randomization of the classical Robinson-Schensted correspondence between words and Young tableaux. Exploring such randomizations we find unexpected applications to six vertex (square ice) type models and traffic systems on a 1-dimensional lattice.

Thu Jan 31

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Jan 31

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Jan 31

## Commutative Algebra Seminar

1:25pm - Vincent Hall 301
Commutative Algebra Seminar

Thu Jan 31

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Jan 31

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Jan 31

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Student Number Theory Seminar

Thu Jan 31

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570
Reading Seminar on Automorphic Forms

Wed Jan 30

## Algebraic Representation Theory Seminar

4:40pm - Vincent Hall 206
Postponed to next week
Peter Webb, University of Minnesota
##### Abstract:

We will start on Section 3 of the paper by Comes and Ostrik, On blocks of Deligne's category Rep(S_t). This will be preceded by a review of the set-up in this category, which is built up out of partition algebras. Section 3 begins with the result that the indecomposable objects are parametrized by partitions of all sizes.

Tue Jan 29

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Jan 29

## Math Physics Seminar

12:20pm - Vincent Hall 209
Higher order superintegrability, Painlevé transcendents and representations of polynomial algebras
Ian Marqutte, University of Queensland
##### Abstract:

I will review results on classification of quantum superintegrable systems on two-dimensional Euclidean space allowing separation of variables in Cartesian coordinates and possessing an extra integral of third or fourth order. The exotic quantum potential satisfy a nonlinear ODE and have been shown to exhibit the Painleve property. I will also present different constructions of higher order superintegrable Hamiltonians involving Painleve transcendents using four types of building blocks which consist of 1D Hamiltonians allowing operators of the type Abelian, Heisenberg, Conformal or Ladder. Their integrals generate finitely generated polynomial algebras and representations can be exploited to calculate the energy spectrum. I will point out that for certain cases associated with exceptional orthogonal polynomials, these algebraic structures do not allow to calculate the full spectrum and degeneracies. I will describe how other sets of integrals can be build and used to provide a complete solution.

Tue Jan 29

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Mon Jan 28

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 207
Automorphic Forms and Number Theory
Postponed
Mon Jan 28

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Jan 28

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Guanglin Xu, University of Minnesota, Twin Cities
Fri Jan 25

## First Year Seminar

6:30pm - Vincent 364
First Year Seminar
TBA, TBA
Fri Jan 25

## MCFAM Seminar

5:30pm - Vincent Hall 16
No MCFAM Seminar

Fri Jan 25

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Jan 25

## Probability Seminar

2:30pm - Vincent Hall 213
Large deviations for sparse random graphs
Nicholas Cook, Stanford University
##### Abstract:

Let $G=G(N,p)$ be an Erd\H{o}s--R\'enyi graph on $N$ vertices (where each pair is connected by an edge independently with probability $p$). We view $N$ as going to infinity, with $p$ possibly going to zero with $N$. What is the probability that $G$ contains twice as many triangles as we would expect? I will discuss recent progress on this infamous upper tail" problem, and more generally on tail estimates for counts of any fixed subgraph. These problems serve as a test bed for the emerging theory of \emph{nonlinear large deviations}, and also connect with issues in extending the theory of \emph{graph limits} to handle sparse graphs. In particular, I will discuss our approach to the upper tail problems via new versions of the classic regularity and counting lemmas from extremal combinatorics, specially tailored to the study of random graphs in the large deviations regime. This talk is based on joint work with Amir Dembo.

Fri Jan 25

## IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Lecture
Eric Lind, Metro Transit
Fri Jan 25

8:30am -
CANCELLED

Thu Jan 24

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Jan 24

## Algebraic Geometry

1:25pm - Vincent Hall 113
Algebraic Geometry Seminar

Thu Jan 24

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club

Thu Jan 24

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Thu Jan 24

## Student Number Theory Seminar

11:00am - Vincent Hall 213
Student Number Theory Seminar

Thu Jan 24

## Reading Seminar on Automorphic Forms

10:00am - Vincent Hall 570
Reading Seminar on Automorphic Forms

Tue Jan 22

## Dynamical Systems

2:30pm - Vincent Hall 313
Dynamical Systems Seminar

Tue Jan 22

## Colloquium

2:30pm - Vincent Hall 16
Multiscale Problems in Cell Biology
Chuan Xue, Ohio State University
##### Abstract:

Complex biological systems involve multiple space and time scales. To get an integrated understanding of these systems involves multiscale modeling, computation and analysis. In this talk, I will discuss two such examples in cell biology and illustrate how to use multiscale methods to explain experimental data. The first example is on chemotaxis of bacterial populations. I will present recent progress on embedding information of single cell dynamics into models of cell population dynamics. I will clarify the scope of validity of the well-known Patlak-Keller-Segel chemotaxis equation and discuss alternative models when it breaks down. The second example is on the axonal cytoskeleton dynamics in health and disease. I will present a stochastic multiscale model that gave the first mechanistic explanation for the cytoskeleton segregation phenomena observed in many neurodegenerative diseases.

Tue Jan 22

## Math Physics Seminar

12:20pm - Vincent Hall 209
Math Physics Seminar

Tue Jan 22

## Climate Seminar

11:15am - Vincent Hall 570
Climate Change Seminar

Mon Jan 21

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri Jan 18

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Jan 18

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Jan 18

8:30am -
CANCELLED

Thu Jan 17

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Jan 15

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Mon Jan 14

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri Jan 11

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Jan 11

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Jan 11

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Algebraic Representation Theory

Fri Jan 11

8:30am -
CANCELLED

Thu Jan 10

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Jan 08

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Mon Jan 07

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri Jan 04

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Jan 04

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Jan 04

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Jan 04

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Algebraic Representation Theory

Fri Jan 04

8:30am -
CANCELLED

Thu Jan 03

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Jan 01

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Mon Dec 31

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri Dec 28

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Dec 28

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Dec 28

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Dec 28

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Algebraic Representation Theory

Fri Dec 28

8:30am -
CANCELLED

Thu Dec 27

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Dec 25

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Mon Dec 24

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Fri Dec 21

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Dec 21

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Dec 21

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Dec 21

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Algebraic Representation Theory

Fri Dec 21

## MathCEP Seminar

10:10am - Vincent Hall 364
MathCEP Seminar

Fri Dec 21

8:30am -
CANCELLED

Thu Dec 20

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Dec 20

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Projective Geometry, Complex Hyperbolic Space, and Geometric Transitions
Steve Trettel, UC Santa Barbara
##### Abstract:

The natural analog of Teichmuller theory for hyperbolic manifolds in dimension 3 or greater is trivialized by Mostow Rigidity, so mathematicians have worked to understand more general deformations. Two well studied examples, convex real projective structures and complex hyperbolic structures, have been investigated extensively and provide independently developed deformation theories. Here we will discuss a surprising connection between the these, and construct a one parameter family of geometries deforming complex hyperbolic space into a new geometry built out of real projective space and its dual. This connects the aforementioned deformation theories and provides geometric motivation for a representation-theoretic observation of Cooper, Long, and Thistlethwaite

Thu Dec 20

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Dec 20

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Dec 20

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Student Number Theory
TBA
Thu Dec 20

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Dec 19

## PDE Seminar

3:30pm - Vincent Hall 570
PDE Seminar

Tue Dec 18

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar

Tue Dec 18

## Math Physics Seminar

12:20pm - Vincent Hall 313
Math Physics Seminar

Tue Dec 18

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Mon Dec 17

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Automorphic Forms and Number Theory

Mon Dec 17

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Dec 17

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: TBA

Mon Dec 17

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Dec 17

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Dec 14

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Dec 14

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Dec 14

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Dec 14

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Dec 14

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Algebraic Representation Theory

Fri Dec 14

## MathCEP Seminar

10:10am - Vincent Hall 364
MathCEP Seminar

Fri Dec 14

8:30am -
CANCELLED

Thu Dec 13

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra Seminar

Thu Dec 13

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Dec 13

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Dec 13

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Dec 13

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Dec 13

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Galois Representations and the Modularity Theorem
Andy Hardt, University of Minnesota
##### Abstract:

I will continue Katy's talk from last week, and talk about chapter 9 of Diamond and Shurman's "A First Course in Modular Forms." We'll define Galois representations corresponding to both elliptic curves and modular forms. Then we'll state the modularity theorem, which asserts that every elliptic curve corresponds to a modular form, and their Galois representations are equal. If we have time, we'll relate this back to the version of the theorem from last week, which equated points on an elliptic curve to Fourier coefficients of a modular form. The proof of the theorem, however, will be left as an exercise to the listener.

Thu Dec 13

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Dec 12

## PDE Seminar

3:35pm - Vincent Hall 570
Scattering for the 3D Gross-Pitaevskii equation
Zihua Guo, Monash University
##### Abstract:

We study the Cauchy problem for the 3D Gross-Pitaevskii equation. Global well-posedness in the natural energy space was proved by Gerard.
We prove scattering for small data in the same space with some additional angular regularity, and in particular in the radial case we obtain small energy scattering.
The crucial ingredients are new generalized Strichartz estimates and some new observed "NULL" structures of the Gross-Pitaevskii equation after some normal form type transform.
This is a joint work with Zaher Hani and Kenji Nakanishi.

Tue Dec 11

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar

Tue Dec 11

## Math Physics Seminar

12:20pm - Vincent Hall 313
Application of Invariant Signatures: Solving Jigsaw Puzzles
Rob Thompson
Tue Dec 11

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Dec 11

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Dec 10

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Automorphic Forms and Number Theory

Mon Dec 10

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Dec 10

## Special Events and Seminars

3:35pm - Vincent Hall 207
Optimal transport on graphs with Applications
Wuchen Li
##### Abstract:

In recent years, optimal transport has many applications in evolutionary dynamics, statistics, and machine learning. In this talk, we introduce dynamical optimal transport on finite graphs. We proposed to study the probability simplex as a Riemannian manifold with a Wasserstein metric. We call it a probability manifold. Various developments, especially the Fokker-Planck equation, will be introduced. The entropy production on graphs related to Shannon entropy will be established. Its connection with Fisher information and Yanos formula will be studied. Many examples, including Mean field games, geometry of graphs, statistical learning problems, will be presented.

Mon Dec 10

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: The geometric average size of Selmer groups over function fields
Aaron Landesman, Stanford
##### Abstract:

We use topological methods to investigate the average size of n-Selmer groups of elliptic curves over F_q(t).
Loosely speaking, the n-Selmer group of an elliptic curve measures objects which look like the n-torsion of the elliptic curve.
We relate the question of computing the average size of the n-Selmer group to demonstrating
homological stability for a sequence of moduli spaces
of these n-Selmer elements.
Via monodromy arguments, we show the number of components of these moduli spaces stabilizes, which determines the
average size after taking a large q limit.

Mon Dec 10

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Dec 10

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Stratifying High-Dimensional Data Based on Proximity to the Convex Hull Boundary
Lori Ziegelmeier, Macalester College
##### Abstract:

The convex hull of a set of points,C, serves to expose extremal properties of C and can help identify elements in C of high interest. For many problems, particularly in the presence of noise, the true vertex set (and facets) may be difficult to determine. One solution is to expand the list of high interest candidates to points lying near the boundary of the convex hull. We propose a quadratic program for the purpose of stratifying points in a data cloud based on proximity to the boundary of the convex hull. For each data point, a quadratic program is solved to determine an associated weight vector. We show that the weight vector encodes geometric information concerning the points relationship to the boundary of the convex hull. The computation of the weight vectors can be carried out in parallel, and for a fixed number of points and fixed neighborhood size, the overall computational complexity of the algorithm grows linearly with dimension. As a consequence, meaningful computations can be completed on reasonably large, high-dimensional data sets.

Lori Ziegelmeier received an A.S. and A.A. from Colby Community College in 2005. She completed her B.S. in Mathematics and B.A. in Liberal Arts and History, M.S. in Mathematics, and Ph.D. in Mathematics all at Colorado State University in 2007, 2009, and 2013, respectively. Since completing her doctoral degree, she has been in the Department of Mathematics, Statistics, and Computer Science at Macalester College and is currently an Assistant Professor. Her research is in the area of geometric and topological data analysis.

Mon Dec 10

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Dec 07

## MCFAM Seminar

5:30pm - Vincent Hall 16
Data Visualization in R
Chen Zhang, Sr. Consultant, Analytics & Research at Travelers; Ph.D. in Statistics from UConn; UMN MFM Alumnus
##### Abstract:

Data visualization is often overlooked by people working with data and/or modeling but can in fact reveal very useful insight into problems at hand. R is an open-source programming language for statistical computing and graphics with increasing popularity among practitioners in data science and machine learning in recent years. The "ggplot2" package in R, in particular, provides very powerful, intuitive and versatile tools for data visualization. An overview of these tools will be presented in this talk accompanied by a live demo.

Fri Dec 07

## Lie Theory Seminar

3:35pm - Vincent Hall 313
Finiteness of Frobenius traces of a de Rham local system
Koji Shimizu, University of California, Berkeley
##### Abstract:

Every smooth projective variety over a number field yields a Galois representation via etale cohomology, and the Weil conjecture tells that its Frobenius traces are integers. Fontaine and Mazur conjectured that Galois representations satisfying a local condition (de Rham) arise from geometry and hence have a similar finiteness property. In this talk, I will focus on de Rham local systems on algebraic varieties and explain a finiteness of Frobenius traces follows from the Fontaine-Mazur conjecture for Galois representations and the generalized Riemann Hypothesis

Fri Dec 07

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Catalan Functions and k-Schur functions
Anna Pun, Drexel University
##### Abstract:

Li-Chung Chen and Mark Haiman studied a family of symmetric functions called Catalan (symmetric) functions which are indexed by pairs consisting of a partition contained in the staircase (n-1, ..., 1,0) (of which there are Catalan many) and a composition weight of length n. They include the Schur functions, the Hall-Littlewood polynomials and their parabolic generalizations. They can be defined by a Demazure-operator formula, and are equal to GL-equivariant Euler characteristics of vector bundles on the flag variety by the Borel-Weil-Bott theorem. We have discovered various properties of Catalan functions, providing a new insight on the existing theorems and conjectures inspired by Macdonald positivity conjecture. A key discovery in our work is an elegant set of ideals of roots that the associated Catalan functions are k-Schur functions and proved that graded k-Schur functions are G-equivariant Euler characteristics of vector bundles on the flag variety, settling a conjecture of Chen-Haiman. We exposed a new shift invariance property of the graded k-Schur functions and resolved the Schur positivity and k-branching conjectures by providing direct combinatorial formulas using strong marked tableaux. We conjectured that Catalan functions with a partition weight are k-Schur positive which strengthens the Schur positivity of Catalan function conjecture by Chen-Haiman and resolved the conjecture with positive combinatorial formulas in cases which capture and refine a variety of problems. This is joint work with Jonah Blasiak, Jennifer Morse and Daniel Summers.

Fri Dec 07

## Topology Seminar

3:30pm - 301 Vincent Hall
Topology Seminar: Power operations in normed motivic spectra
Tom Bachmann, MIT
##### Abstract:

In joint work with M. Hoyois, we established (the beginnings of) a theory of "normed motivic spectra". These are motivic spectra with some extra structure, enhancing the standard notion of a motivic E_oo-ring spectrum (this is similar to the notion of G-commutative ring spectra in equivariant stable homotopy theory). It was clear from the beginning that the homotopy groups of such normed spectra afford interesting *power operations*. In ongoing joint work with E. Elmanto and J. Heller, we attempt to establish a theory of these operations and exploit them calculationally. I will report on this, and more specifically on our proof of a weak motivic analog of the following classical result of Würgler: any (homotopy) ring spectrum with 2=0 is generalized Eilenberg-MacLane.

Fri Dec 07

## Probability Seminar

2:30pm - Vincent Hall 209
When particle systems meet PDEs
Li-Cheng Tsai, Columbia University
##### Abstract:

Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three paradigmatic facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems.

Fri Dec 07

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Dec 07

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
The definition of Deligne's category Rep(S_t) - continuation
Cecily Santiago, University of Minnesota
##### Abstract:

We will complete the steps in the definition of Deligne's category described in section 2.2 of the paper, On blocks of Deligne's category Rep(S_t), by Comes and Ostrik.

Fri Dec 07

## IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
When Seeing is not Believing: New Forensics Algorithms to Detect Image Manipulations
Michael Albright, Honeywell
##### Abstract:

Modern image editing software has made it possible to alter images in ways that can dramatically change the image content, yet the images may appear authentic to humans. While there are countless beneficial applications of photo editing, image manipulations can also be used in harmful ways  e.g., altered images may be published to cause reputational harm, sway public opinions, influence elections, etc. Furthermore, with the growing popularity of social media and online sharing platforms, it is increasingly easy for altered media to go viral. Whats more, recent breakthroughs in artificial intelligence (AI) are making it dramatically easier to produce altered images, and even altered videos, that appear photo realistic. Hence, there is growing interest in developing new forensic methods that can detect manipulations in images and video. In this talk, I will give an overview of my teams work on the DARPA-funded Media Forensics (MediFor) Project to develop novel machine-learning algorithms for automated detection and localization of media manipulations.

Michael Albright is a senior data scientist in the Data Science and Video Analytics group in Honeywell Labs in Golden Valley, Minnesota. Since joining Honeywell in 2015, he has invented new technologies that solve challenging problems for internal Honeywell businesses and external customers. His work has involved applying machine learning, optimization, and other applied math and computer science techniques to a variety of problems in domains ranging from Internet of Things (IoT) systems to computer vision applications. Michael earned a Ph.D. in theoretical physics from the University of Minnesota in 2015 and has previous industry experience at Cray, Inc.

Fri Dec 07

## MathCEP Seminar

10:10am - Vincent Hall 364
Experiments in STEM Education
Michelle Driessen, University of Minnesota
##### Abstract:

The general chemistry program has been experimenting with several new pedagogies in order to improve student learning and successful outcomes. Ill begin with our placement system and new adaptive courseware/learning analytics project, and will discuss any other project as time allows.

1. ALEKS Placement/Learning Modules
2. Adaptive Courseware (Smart Sparrow)
Using Adaptivity and Learning Analytics to Identify At-Risk Students and Implement Early Interventions
3. Absolute grading in 1061
Six Lower-Stakes Exams + Final
E-proctored Exams  available over a 12 hour window
4. Credit/No Credit Grading in Lab Courses + Specifications Grading

Fri Dec 07

8:30am -
CANCELLED

Thu Dec 06

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra Seminar

Thu Dec 06

## Colloquium

3:35pm - Vincent Hall 16
Number theory over function fields and geometry
Will Sawin, Columbia University
##### Abstract:

The function field model involves taking problems in
classical analytic number theory and replacing the integers with
polynomials over a finite field. This preserves most of the complexity
of these problems while giving them a stronger relationship to
geometry, allowing new techniques to be applied. We will explain how
this works using a recent example involving sums of the divisor
function where, thanks to good luck, particularly simple methods can
prove a particularly powerful result.

Thu Dec 06

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Enumerative geometry: old and new
Felix Janda, University of Michigan
##### Abstract:

For as long as people have studied geometry, they have counted
geometric objects. For example, Euclid's Elements starts with the
postulate that there is exactly one line passing through two distinct
points in the plane. Since then, the kinds of counting problems we are
able to pose and to answer has grown. Today enumerative geometry is a
rich subject with connections to many fields, including combinatorics,
physics, representation theory, number theory and integrable systems.

In this talk, I will show how to solve several classical counting
questions. Then I will describe a more modern problem with roots in
string theory which has been the subject of intense study for the last
two decades, namely the study of the Gromov-Witten invariants of the
quintic threefold, a Calabi-Yau manifold. I will explain a recent
break-through in understanding the higher genus invariants that stems
from a seemingly unrelated problem related to the study of holomorphic
differentials on Riemann surfaces.

Thu Dec 06

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Dec 06

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Dec 06

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
A Tour of the Modularity Theorem
Katy Weber, University of Minnesota
##### Abstract:

The Modularity Theorem (also known as the Taniyama-Shimura-Weil Conjecture) states, essentially, that every elliptic curve arises from a modular form. It is a special case of the Langlands correspondence and was a major part of Andrew Wiles' proof of Fermat's Last Theorem. In this talk, I will sketchily discuss the theorem in its various forms, leading up to the statement that the L-function of an elliptic curve agrees with the L-function of a modular form. Along the way, we will encounter some algebraic geometry words, e.g. "moduli space," "universal curve," and "sheaf."

Thu Dec 06

## Climate Seminar

11:15am - Vincent Hall 570
Stability of traveling pulses in the FitzHugh--Nagumo equations
Paul Carter, University of Arizona
##### Abstract:

Traveling waves arise in partial differential equations in a broad range of applications, for instance chemical reactions, propagation of electrical signals, or the dynamics of traffic jams. The notion of stability of a traveling wave solution concerns its resilience to small perturbations and can usually be inferred from an eigenvalue problem obtained by linearizing the PDE about the solution. In this talk, I will discuss these ideas in the context of the FitzHugh--Nagumo system, a simplified model of nerve impulse propagation. I will present existence and stability results for (multi)pulse solutions, and I will describe a phenomenon whereby unstable eigenvalues accumulate as a single pulse is continuously deformed into a double pulse

Thu Dec 06

## Special Events and Seminars

11:00am - Tate Hall B20
p-adic local systems in p-adic geometry
Koji Shimizu, University of California, Berkeley
##### Abstract:

An etale p-adic local system on a rigid analytic variety can be regarded as a family of p-adic Galois representations parametrized by the variety, and p-adic Hodge theory has brought many results and applications on such objects, including a p-adic Riemann-Hilbert correspondence by Diao, Lan, Liu and Zhu. I will discuss constancy of a key invariant (generalized Hodge-Tate weights) of general p-adic local systems

Wed Dec 05

## PDE Seminar

3:35pm - Vincent Hall 570
Barotropic instability of shear flows
Zhiwu Lin, Georgia Institute of Technology
##### Abstract:

We consider barotropic instability of shear flows for incompressible fluids with Coriolis effects. For a class of shear flows, we develop an approach by using the Hamiltonian structures of the linearized equation and an instability index formula to find the sharp stability conditions. We studied the flow with Sinus profile in details and found the sharp stability boundary in the whole parameter space, which corrected previous results in the fluid literature. The addition of the Coriolis force brings some fundamental changes to the stability of shear flows. Moreover, we also study the bifurcation of nontrivial traveling wave solutions and the linear inviscid damping near the shear flows. This is joint work with Hao Zhu and Jincheng Yang.

Tue Dec 04

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar

Tue Dec 04

## Math Physics Seminar

12:20pm - Vincent Hall 313
Revivals and Fractalization in the Linear Free Space Schrödinger Equation with Pseudoperiodic Boundary Conditions
Natalie Sheils
##### Abstract:

We consider the one-dimensional linear free space Schrödinger equation on a bounded interval subject to homogeneous linear boundary conditions. We prove that, in the case of pseudoperiodic boundary conditions, the solution of the initial-boundary value problem exhibits the phenomenon of revival at specific ("rational'') times, meaning that it is a linear combination of a certain number of copies of the initial datum. Equivalently, the fundamental solution at these times is a finite linear combination of delta functions. At other ("irrational'') times, for suitably rough initial data, e.g., a step or more general piecewise constant function, the solution exhibits a continuous but fractal-like profile. Further, we express the solution for general homogeneous linear boundary conditions in terms of numerically computable eigenfunctions. (Joint work with Peter Olver and David Smith)

Tue Dec 04

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Dec 04

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Dec 03

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
A Chebotarev density theorem for families of fields with an application to bounding l-torsion in class groups
Caroline Turnage-Butterbaugh
Mon Dec 03

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Interfaces with singularities: understanding phase transitions in nematic liquid crystals
Dmitry Golovaty, Department of Mathematics, University of Akron
##### Abstract:

A nematic liquid crystal is essentially a liquid that exhibits some orientational order. The liquid crystalline state is typically observed in materials composed of highly asymmetric molecules for temperatures in the intermediate range when the material is neither a classical liquid nor a solid. In this talk we will be interested in describing a phase transition between the nematic and the isotopic state when the nematic order melts and the liquid crystal turns into a regular isotopic fluid. The experimental observations of this process indicate that the transition proceeds via evolution of interfaces separating different phases where the interfaces are generally not smooth. Our goal in this talk is to explain presence of these phase boundary singularities from a mathematical point of view .

The nematic-to-isotopic phase transition can be described within the so called Landau-de Genes variational theory for a tensor-valued order parameter. Because this theory is rather complex, in order to develop an initial understanding of transitions between the ordered and disordered states, we propose a simpler toy model based on the modified Ginzburg-Landau-type energy defined over vector fields on the plane. The corresponding variational model consists of anisotropic gradient terms and a potential that vanishes on two disconnected sets. While this model may not quantitatively describe the nematic state, the topology of the simplified target set retains the crucial features of the full problem. The principal observation from the study of the simplified model is that the phase boundary singularities can be explained by large disparity between the elastic constants that specify the gradient contribution to the energy. In the talk we will present a combination of rigorous analysis and numerics that leads to this conclusion.

Mon Dec 03

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Dec 03

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Nov 30

## MCFAM Seminar

5:30pm - Vincent Hall 16
The Effect of the Risk Corridors Program on Marketplace Premiums and Participation
Pinar Karaca Mandic, MILI Director/Carlson Finance Professor
##### Abstract:

We investigate the effect of the Risk Corridors (RC) program
on premiums and insurer participation in the Affordable Care Act
(ACA)s Health Insurance Marketplaces. The RC program, which was
defunded ahead of coverage year 2016, and ended in 2017, is a risk
sharing mechanism: it makes payments to insurers whose costs are high
relative to their revenue, and collects payments from insurers whose
costs are relatively low. We show theoretically that the RC program
creates strong incentives to lower premiums for some insurers.
Empirically, we find that insurers who claimed RC payments in 2015,
before defunding, had greater premium increases in 2017, after the
program ended. Insurance markets in which more insurers made RC claims
experienced larger premium increases after the program ended,
reflecting equilibrium effects. We do not find robust evidence that
insurers with larger RC claims in 2015 were less likely to participate
in the ACA Marketplaces in 2016 and 2017. Overall we find that the end
of the RC program significantly contributed to premium growth.

Fri Nov 30

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Grassmann Pentagram Maps and Non-commutative Integrable Systems
Nicholas Ovenhouse, Michigan State University
##### Abstract:

The pentagram map is a discrete dynamical system on the space of plane polygons. Gekhtman, Shapiro, Tabachnikov, and Vainshtein used the combinatorics and Poisson geometry associated to certain networks/quivers on surfaces to prove that this map is integrable. Recently, Mari-Beffa and Felipe introduced a version of the pentagram map on Grassmannians, and found a Lax representation. I will generalize the techniques of Gekhtman et. al. to the Grassmann case, and show this gives a "formal" integrable system in a non-commutative algebra.

Fri Nov 30

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Nov 30

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Nov 30

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Nov 30

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
The definition of Deligne's category Rep(S_t)
Cecily Santiago, University of Minnesota
##### Abstract:

Following section 2.2 of the paper, On blocks of Deligne's category Rep(S_t), by Comes and Ostrik, we give the definition of this category and explore some of its first properties.

Fri Nov 30

## IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Recap of MinneMUDAC: Challenges and Improvements
-, -
##### Abstract:

Graduate-level participants of 2018 MinneMUDAC data challenge will give an updated version of their original presentation, supplemented with suggestions for potential improvements to answering the challenge question, which was predicting the voter turnout for the 2018 midterm elections in Minnesota. After the talks, all participants will break into discussions regarding the presentations and the questions that arise from them.

Speakers: Several teams that competed in MinneMUDAC

Fri Nov 30

## MathCEP Seminar

10:10am - Vincent Hall 364
MathCEP Seminar

Fri Nov 30

8:30am -
CANCELLED

Thu Nov 29

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra Seminar

Thu Nov 29

## Colloquium

3:35pm - Vincent Hall 16
Interpolative decomposition and its applications
Lexing Ying, Stanford, Ordway Visitor
##### Abstract:

Interpolative decomposition is a simple and yet powerful tool for approximating low-rank matrices. After discussing the theory and algorithm, I will present a few new applications of interpolative decomposition in numerical partial differential equations, quantum chemistry, and machine learning.

Thu Nov 29

## IMA Data Science Lab Seminar

3:35pm - Vincent 16
Interpolative Decomposition and its Applications (Math Dept Colloquium Lecture)
Lexing Ying, Stanford University
##### Abstract:

Interpolative decomposition is a simple and yet powerful tool for approximating low-rank matrices. After discussing the theory and algorithm, I will present a few new applications of interpolative decomposition in numerical partial differential equations, quantum chemistry, and machine learning.

Thu Nov 29

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Nov 29

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
On invariant theory for "coincidental" reflection groups
Victor Reiner, University of Minnesota
##### Abstract:

(joint work with A. Shepler and E. Sommers)
Complex reflection groups W are the finite subgroups of GL_n(C) with the following property: when they act on polynomials in n variables, their invariant ring is again a polynomial algebra. It is also known by
a result of Eagon and Hochster that, for any of their W-representations U, the U-isotypic polynomials form a _free_ module over the W-invariant subalgebra. In a few cases, we know an explicit basis for these U-isotypic polynomials. This talk will discuss a class of complex reflection groups W, sometimes called the "coincidental types", where conjecturally we know explicit bases for the U-isotypic component when U is any tensor product of the exterior powers of the reflection representation and its dual. This conjecture would explain pleasant product formulas for combinatorial objects, such as face numbers for finite type cluster complexes.

Thu Nov 29

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Nov 29

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
The Weil Conjectures: 0 to 100
Liam Keenan, University of Minnesota
##### Abstract:

The Weil conjectures are perhaps one of the most stunning achievements in arithmetic geometry in the 20th century. In this talk, I plan to introduce the necessary algebro-geometric language, state the conjectures, discuss the some of the tools used to prove them, and draw connections to analytic number theory.

Thu Nov 29

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Thu Nov 29

## Colloquium

10:00am - Vincent Hall 570
The role of Energy in Regularity
Max Engelstein, MIT
##### Abstract:

The calculus of variations asks us to minimize some energy and then describe the shape/properties of the minimizers. It is perhaps a surprising fact that minimizers to nice" energies are more regular than one, a priori, assumes. A useful tool for understanding this phenomenon is the Euler-Lagrange equation, which is a partial differential equation satisfied by the critical points of the energy.

However, as we teach our calculus students, not every critical point is a minimizer. In this talk we will discuss some techniques to distinguish the behavior of general critical points from that of minimizers. We will then outline how these techniques may be used to solve some central open problems in the field.

We will then turn the tables, and examine PDEs which look like they should be an Euler-Lagrange equation but for which there is no underlying energy. For some of these PDEs the solutions will regularize (as if there were an underlying energy) for others, pathological behavior can occur

Wed Nov 28

## PDE Seminar

3:30pm - Vincent Hall 570
An Epiperimetric Approach to Isolated Singularities
Max Engelstein, MIT
##### Abstract:

The presence of singular points (i.e. points around which the object in question does not look flat at any scale) is inevitable in most minimization problems. One fundamental question is whether minimizers have a unique tangent object at singular points i.e., is the minimizer increasingly well approximated by some other minimizing object as we zoom in at a singular point. This question has been investigated with varying degrees of success in the settings of minimal surfaces, harmonic maps and obstacle problems amongst others.

In this talk, we will give the first uniqueness of blowups result for minimizers of the Alt-Caffarelli functional. In particular, we prove that the tangent object is unique at isolated singular points in the free boundary. Our main tool is a new approach to proving (log-)epiperimetric inequalities at isolated singularities. This epiperimetric inequality differs from previous ones in that it holds without any additional assumptions on the symmetries of the tangent object.

If we have time, we will also discuss how this method allows us to recover some uniqueness of blow-ups results in the minimal surfaces setting, particularly those of Allard-Almgren (81) and Leon Simon (83). This is joint work with Luca Spolaor (MIT) and Bozhidar Velichkov (U. Grenoble Alpes).

Wed Nov 28

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Convex Relaxation Approaches for Strictly Correlated Density Functional Theory
Lexing Ying, Stanford University
##### Abstract:

In this talk, we introduce methods from convex optimization to solve the multi-marginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of N-representable 2-marginals and 3-marginals, which in turn provide lower bounds to the energy. We further propose rounding schemes to obtain upper bound to the energy.

Tue Nov 27

## Colloquium

3:35pm - Vincent Hall 16
Surface bundles, monodromy, and arithmetic groups
Bena Tshishiku, Harvard University
##### Abstract:

Fiber bundles with fiber a surface arise in many areas including hyperbolic geometry, symplectic geometry, and algebraic geometry. Up to isomorphism, a surface bundle is completely determined by its monodromy representation, which is a homomorphism to a mapping class group. This allows one to use algebra to study the topology of surface bundles. Unfortunately, the monodromy representation is typically difficult to "compute" (e.g. determine its image). In this talk, I will discuss some recent work toward computing monodromy groups for holomorphic surface bundles, including certain examples of Atiyah and Kodaira. This can be applied to the problem of counting the number of ways that certain 4-manifolds fiber over a surface. This is joint work with Nick Salter.

Tue Nov 27

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar - Eddie Nijholt - Cancelled
Eddie Nijholt, UIUC
##### Abstract:

Network dynamical systems play an important role in many fields of science; whenever there are agents whose time evolution is linked through some interaction structure, we may view the system as a network and model it accordingly. However, despite their prevalence, network dynamical systems are in general not well understood. One can identify two reasons for this. First of all, many coordinate changes and other transformations from well-known dynamical systems techniques do not respect the underlying network structure. Second of all, despite this somewhat ethereal' character, systems with a network structure often display behavior that is highly anomalous for general dynamical systems. Examples of this include very unusual bifurcation scenarios and high spectral degeneracies. As a possible explanation of this, it can be shown that a large class of network ODEs admit hidden symmetry, which may be discovered through the so-called fundamental network construction. In most cases, this underlying symmetry does not come from a group though, but rather from a more general algebraic structure such as a monoid or category. I will show how the fundamental network allows one to adapt techniques from dynamical systems theory to a network setting, and how some of the more unusual properties of networks may be explained. In doing so, I will mostly focus on spectral properties of linear network maps.

Tue Nov 27

## Math Physics Seminar

12:20pm - Vincent Hall 313
Math Physics Seminar

Tue Nov 27

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Nov 27

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Nov 26

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Cuspforms with Compact Support [sic]
Paul Garrett, University of Minnesota
Mon Nov 26

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Nov 26

## Special Events and Seminars

3:35pm - Vincent Hall 207
Inverse transport theory and related applications
Ru-Yu Lai, University of Minnesota
##### Abstract:

The inverse transport problem consists of reconstructing the optical properties of a medium from boundary measurements. It finds applications in a variety of fields. In particular, radiative transfer equation (a linear transport equation) models the photon propagation in a medium in optical tomography. In this talk I will address results on the determination of these optical parameters. Moreover, the connection between the inverse transport problem and the Calderon problem will also be presented.

Mon Nov 26

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: Cohomology of arithmetic groups and characteristic classes of manifold bundles
Bena Tshishiku, Harvard University
##### Abstract:

A basic problem in the study of fiber bundles is to compute the ring H*(BDiff(M)) of characteristic classes of bundles with fiber a smooth manifold M. When M is a surface, this problem has ties to algebraic topology, geometric group theory, and algebraic geometry. We have a good understanding of the cohomology in the "stable range", but this accounts for a small percentage of the total cohomology, and little is known beyond that. In this talk I describe some new characteristic classes (in the case dim M >>0) that come from the unstable cohomology of arithmetic groups.

Mon Nov 26

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Nov 26

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Solving PDEs with Deep Learning
Lexing Ying, Stanford University
##### Abstract:

In this talk, I will discuss some recent work on using deep neutral networks in solving high dimensional PDE problems. Examples include molecular dynamics, density functional theory, and inverse scattering problems. In each case, we propose novel neural network architectures based on the physical properties and sparse structures of the problem under investigation.

Mon Nov 26

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Nov 23

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Nov 23

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Combinatorics Seminar

Fri Nov 23

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Nov 23

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Nov 23

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Nov 23

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Algebraic Representation Theory

Fri Nov 23

## MathCEP Seminar

10:10am - Vincent Hall 364
MathCEP Seminar

Fri Nov 23

8:30am -
CANCELLED

Thu Nov 22

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra Seminar

Thu Nov 22

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Nov 22

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Nov 22

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Nov 22

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Nov 22

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Student Number Theory
TBA
Thu Nov 22

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Nov 21

## PDE Seminar

3:30pm - Vincent Hall 570
PDE Seminar

Tue Nov 20

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar

Tue Nov 20

## Math Physics Seminar

12:20pm - Vincent Hall 313
Application of Invariant Signatures: Solving Jigsaw Puzzles
Rob Thompson

TBA

Tue Nov 20

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Nov 20

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Nov 19

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Semigroups and automorphic forms
Amy DeCelles, University of St. Thomas
Mon Nov 19

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Divide and conquer algorithms and software for large Hermitian eigenvalue problems
Yousef Saad, Department of Computer Science and Engineering, University of Minnesota
##### Abstract:

The solution of large symmetric real (or Hermitian complex) eigenvalue
problems is central to applications ranging from electronic structure
calculations to the study of vibrations in mechanical systems. A few
of these applications require the computation of a large number of
eigenvalues and associated eigenvectors. For example, when dealing
with excited states in quantum mechanics, it is not uncommon to seek a
few tens of thousands of eigenvalues of matrices of sizes in the tens
of millions. In such situations it is imperative to resort to
spectrum slicing' strategies, i.e., strategies that extract slices of
the spectrum independently. The presentation will discuss a few of
these techniques that are based on a combination of filtering
(polynomial, rational) and standard projection methods (Lanczos,
subspace iteration). The talk will also discuss our recently released
code named EVSL (for eigenvalues slicing library) that implements
these ideas.

Mon Nov 19

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: The spectrum of units of a height 2 theory
Jeremy Hahn, Harvard University
##### Abstract:

The space BSU admits two infinite loop space structures, one arising from addition of vector bundles and the other from tensor product. A surprising fact, due to Adams and Priddy, is that these two infinite loop spaces become equivalent after p-completion. I will explain how the Adams-Priddy theorem allows for an identification of sl_1(ku_p), the spectrum of units of p-complete complex K-theory. I will then describe work, joint with Andrew Senger, that attempts to similarly understand the spectrum of units of the 2-completion of tmf_1(3).

Mon Nov 19

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Nov 19

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lipschitz Regularized Deep Neural Networks Converge and are Robust to Adversarial Perturbations
Adam Oberman, McGill University
##### Abstract:

Deep Neural Networks perform well in practice, but unlike traditional Machine Learning methods, they lack performance guarantees. This limits the use of the technology in real world and real time applications. The first step towards these guarantees is a proof of generalization. We will prove that Lipschitz regularized DNNs converge, and provide a rate of convergence, a stronger result which implies generalization. The regularization is related to the classical Lipschitz extension problem, and to inverse problems in Image Processing. It can be implemented in practice, and leads to robust networks which are more resistant to adversarial examples.

Joint work with Jeff Calder, available at https://arxiv.org/abs/1808.09540

Adam Oberman in a professor at McGill University. He studied at University of Toronto (Bachelors) and University of Chicago (PhD) before a postdoc at University of Texas, Austin, and a faculty position at Simon Fraser University. His research is on numerical methods for Partial Differential Equations, and more recently on optimization and Machine Learning.

Mon Nov 19

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Nov 16

## MCFAM Seminar

5:30pm - Vincent Hall 16
No MCFAM Seminar

Fri Nov 16

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Cyclic Sieving, Necklaces, and Bracelets
Eric Stucky, University of Minnesota
##### Abstract:

One of the many interpretations of Catalan numbers is that Cn counts necklaces with n white beads and n+1 black beads. Motivated by this, we generalize the Catalan numbers and their q-analogues to many other necklaces. In this talk, we will discuss two surprising properties of these generalizations. First, they exhibit a q=-1 phenomenon with respect to necklace reflection, which can be extended to a cyclic sieving phenomenon for more exotic symmetries. Second, they conjecturally satisfy a "parity-unimodality" property, which in classical cases is a combinatorial shadow of a certain sl2 representation.

Fri Nov 16

## Probability Seminar

2:30pm - Vincent Hall 209
Macroscopic fluctuations through Schur generating functions
Vadim Gorin, MIT
##### Abstract:

I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.
It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.

Fri Nov 16

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Nov 16

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Nov 16

## IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Advanced Dynamics Systems Analysis and Synthesis for Future Storage Challenges
Raye Sosseh, Seagate Technology
##### Abstract:

Seagate is the global leader in data storage solutions, developing amazing products that enable people and businesses around the world to create, share and preserve their most critical memories and business data. Over the years the amount of information stored has grown from megabytes all the way to geopbytes, confirming the need to successfully store and access huge amounts of data. As demand for storage technology grows the need for greater efficiency and more advanced capabilities continues to evolve. Today data storage is more than just archiving; its about providing ways to analyze information, understand patterns and behavior, to re-live experiences and memories. Its about harnessing stored information for growth and innovation. Seagate is building on its heritage of storage leadership to solve the challenge of getting more out of the living information thats produced everyday. What began with one storage innovation has morphed into many systems and solutions becoming faster, more reliable and expansive. These considerations will be explored in this lecture on the application of Advanced Dynamics System Analysis & Synthesis to provide Solutions for future Storage Challenges.

Bio
Dr. Raye A. Sosseh is a managing Principal engineer and leads the Advanced Dynamics Group in Seagates Advanced Product Development department. His background is in dynamics and controls of embedded systems with particular applications to Hard Disk Drives. Dr. Sosseh holds a Ph.D. in Mechanical Engineering and a Masters in Electrical Engineering from the Georgia Institute of Technology. He joined Seagate in 2001 and has contributed to the staging and development of numerous products in Seagates Mission Critical and Cloud solutions swimlanes. Dr. Sosseh has over 10 patents assigned and pending patents. Raye and his family enjoy the lakes and restaurants in the Minneapolis area.

Fri Nov 16

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Partition algebras and their action on tensor space - continuation
Weiyan Chen, University of Minnesota
##### Abstract:

We continue with section 2.1 of the paper, On blocks of Delignes category Rep(S_t), by Comes and Ostrik. The longer term goal is to describe Deligne's category. In section 2.1 the partition algebras are introduced. They arose in work of Martin in a context of statistical mechanics, and were later shown by Jones to be in Schur-Weyl duality with the group algebras of symmetric groups. The exposition is introductory.

Fri Nov 16

## MathCEP Seminar

10:10am - Vincent Hall 364
MathCEP Seminar

Fri Nov 16

8:30am -
CANCELLED

Thu Nov 15

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra Seminar

Thu Nov 15

## Colloquium

3:35pm - Vincent Hall 16
(Log)-Epiperimetric Inequality and the Regularity of Variational Problems
Luca Spolaor, MIT
##### Abstract:

In this talk I will present a new method for studying the regularity of minimizers to variational problems. I will start by introducing the notion of blow-up, using as a model case the so-called Obstacle problem. Then I will state the (Log)-epiperimetric inequality and explain how it is used to prove uniqueness of the blow-up and regularity results for the solution near its singular set. I will then show the flexibility of this method by describing how it can be applied to other free-boundary problems and to (almost)-area minimizing currents. Finally I will describe some future applications of this method both in regularity theory and in other settings.

Thu Nov 15

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Nov 15

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Nov 15

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Nov 15

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Physics of the Riemann-zeta function II
Adrienne Sands, University of Minnesota
##### Abstract:

We continue to discuss how the Riemann-zeta function plays a role in different areas of physics, from condensed matter theory to quantum mechanics

Thu Nov 15

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Nov 14

## PDE Seminar

3:30pm - Vincent Hall 570
PDE Seminar

Tue Nov 13

## Dynamical Systems

2:30pm - Ford Hall 130
Zigzagging of stripe patterns in growing domains
Montie Avery, University of Minnesota
##### Abstract:

The Swift-Hohenberg equation is a PDE which models formation of stripe and spot patterns in many physical settings. I will study a modification in which pattern formation is triggered by a propagating interface, and discuss the bifurcation structure based on the interface speed. I will focus on analytical results in reduced equations, in particular a singular perturbation problem for a system of ODEs arising from a traveling wave ansatz. I will also present numerical results in the Swift-Hohenberg and reduced equations which organize the bifurcation structure into a two-dimensional surface we call the moduli space. This is joint work with Ryah Goh, Oscar Goodloe, Alex Milewski, and Arnd Scheel.

Tue Nov 13

## Math Physics Seminar

12:20pm - Vincent Hall 313
Math Physics Seminar

Tue Nov 13

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Nov 13

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Nov 12

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Semigroups and uniqueness of solutions of differential equations in automorphic forms
Amy DeCelles, University of St. Thomas
Mon Nov 12

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Nov 12

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: Localizing the E_2 page of the Adams spectral sequence
Eva Belmont, Northwestern
##### Abstract:

The Adams spectral sequence is one of the central tools for calculating the stable homotopy groups of spheres, one of the motivating problems in stable homotopy theory. In this talk, I will discuss an approach for computing the Adams E_2 page for the sphere at p = 3 in an infinite region, by computing its localization by the non-nilpotent element b_{10}. This approach relies on computing an analogue of the Adams spectral sequence in Palmieri's stable category of comodules, which can be regarded as an algebraic analogue of stable homotopy theory. This computation fits in the framework of chromatic homotopy theory in the stable category of comodules.

Mon Nov 12

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Nov 12

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Rebecca Willett, University of Chicago
Mon Nov 12

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Nov 09

## MCFAM Seminar

5:30pm - Vincent Hall 16
Macroecomic Analysis and Insight - Steepness of the Yield Curve As of September 2018
Ujae Kang, UnitedHealth Group
##### Abstract:

Ujae Kang will present on the Federal Reserve over the years and its influence on the yield curve. Then, he will cover what to expect from the Federal Reserve in the coming years.

Bio: Ujae Kang is Director of Enterprise Risk Management at UnitedHealth Group. He is an Associate of the Society of Actuaries and has an Master of Financial Mathematics from the University of Minnesota's School of Mathematics. He also provides economic research and insights to UnitedHealth Group's Asset Liability Management Committee as well as to other investors. For more information on Ujae go to linkedin.com/in/ujaeaugustinekang

Fri Nov 09

## Lie Theory Seminar

3:35pm - Vincent Hall 313
Motivic cohomology of Shimura varieties and level raising
Rong Zhou, Institute for Advanced Study
##### Abstract:

For a finite type scheme over a field, its motivic cohomology groups were defined by Voevodsky and are an important algebraic invariant. However, the properties of these groups are not well understood, and it is a difficult problem to exhibit explicit classes in motivic cohomology. We will construct such classes in the special fiber of Hilbert modular varieties by using the geometry of the supersingular locus. The construction is related to a geometric realization of the Jacquet-Langlands correspondence, as well as to level raising for Hilbert modular forms. A key ingredient is a form of Ihara's Lemma for compact quaternionic Shimura surfaces.

Fri Nov 09

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Combinatorics Seminar

Fri Nov 09

## Probability Seminar

2:30pm - Vincent Hall 209
Low-temperature localization of directed polymers
Erik Bates, Stanford University
##### Abstract:

On the d-dimensional integer lattice, directed polymers are paths of a random walk that have been reweighted according to a random environment that refreshes at each time step. The qualitative behavior of the system is governed by a temperature parameter; if this parameter is small, the environment has little effect, meaning all possible paths are close to equally likely. If the parameter is made large, however, the system undergoes a phase transition at which the paths endpoint starts to localize. To understand the extent of this localization, we exploit the underlying Markov structure of the quenched endpoint distribution. The key difficulty is that the space of measures is too large for one to expect convergence results. By adapting methods appearing in the work of Mukherjee and Varadhan, we develop a compactification theory to resolve the issue. In this talk, we will discuss this intriguing abstraction, as well as new concrete theorems it allows us to prove for directed polymers constructed from SRW or any other walk. (joint work with Sourav Chatterjee)

Fri Nov 09

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Nov 09

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Partition algebras and their action on tensor space
Weiyan Chen, University of Minnesota
##### Abstract:

We follow section 2.1 of the paper, On blocks of Delignes category Rep(S_t), by Comes and Ostrik. The longer term goal is to describe Deligne's category. In section 2.1 the partition algebras are introduced. They arose in work of Martin in a context of statistical mechanics, and were later shown by Jones to be in Schur-Weyl duality with the group algebras of symmetric groups. We introduce this theory.

Fri Nov 09

## MathCEP Seminar

10:10am - Vincent Hall 364
The Distributed Open Education Network (Doenet) and your dream educational technology
Duane Nykamp, University of Minnesota
##### Abstract:

A group of us are developing educational technology as part of the
Distributed Open Education Network (Doenet). We'll describe our vision for
an open educational technology ecosystem and highlight some solutions that
we are currently implementing. Then, we'll open the floor to discuss your
dreams for technological innovations that will enable you to better help
students learn.

Fri Nov 09

8:30am -
CANCELLED

Thu Nov 08

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra Seminar

Thu Nov 08

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Nov 08

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Nov 08

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Nov 08

## Special Events and Seminars

1:25pm - Vincent Hall 313
Irreducible components of affine Deligne--Lusztig varieties and orbital integrals
Rong Zhou, Institute for Advanced Study
##### Abstract:

Affine Deligne--Lusztig varieties (ADLV) naturally arise in the study of Shimura varieties and Rapoport--Zink spaces. Their irreducible components provide an interesting class of cycles on the special fiber of Shimura varieties. We prove a conjecture of Miaofen Chen and Xinwen Zhu, which relates the number of irreducible components of ADLV's to a certain weight multiplicity for a representation of the Langlands dual group. Our approach is to count the number of F_q points as q goes to infinity; this boils down to computing a certain twisted orbital integral. After applying techniques from local harmonic analysis, we reduce to computing a particular coefficient of the matrix for the inverse Satake transform. Using an interpretation of this coefficient in terms of a q-analogue of Kostant's partition function, we are able to reduce the problem to the previously known special cases of the conjecture proved by Hamacher--Viehmann and Nie. This is joint work with Yihang Zhu.

Thu Nov 08

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Nov 08

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Physics of the Riemann-zeta function
Adrienne Sands, University of Minnesota
##### Abstract:

I will give an overview of how the Riemann-zeta function plays a role in different areas of physics, from condensed matter theory to quantum mechanics.

Thu Nov 08

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Nov 07

## PDE Seminar

3:30pm - Vincent Hall 570
PDE Seminar

Tue Nov 06

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar

Tue Nov 06

## Math Physics Seminar

12:20pm - Vincent Hall 313
Contact Point Forces Acting on a Ball, Rolling on a Horizontal Plane and Actuated by Internal Point Masses
Stuart Rogers
##### Abstract:

This talk derives the contact point forces, namely the normal force and static friction, that act on a ball rolling without slipping on a horizontal plane. It is assumed that the ball is actuated by n point masses, which are free to move inside the ball. The dynamics of a disk and ball actuated by internal point masses are simulated numerically and the minimum coefficients of static friction required to prevent slippage are computed

Tue Nov 06

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Nov 06

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Nov 05

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Semigroups and uniqueness argument for solutions of differential equations in automorphic forms
Amy DeCelles, St. Thomas University
Mon Nov 05

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Nov 05

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: An isovariant Elmendorf's theorem
Sarah Yeakel, University of Maryland
##### Abstract:

An isovariant map is an equivariant map which preserves isotropy groups. Isovariant maps show up in equivariant surgery theory and in other settings when homotopy theory is applied to geometry. For a finite group G, we consider the category of G-spaces with morphisms given by isovariant maps. We will discuss a cofibrantly generated model structure on this category, along with isovariant versions of Elmendorf's theorem and a theorem of Klein and Williams about homotoping a map off a submanifold.

Mon Nov 05

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Nov 05

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Matthew Jacobs, University of California, Los Angeles
Mon Nov 05

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Nov 02

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Nov 02

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Enumerating factorizations in GL_n(F_q)
Graham Gordon, University of Washington
##### Abstract:

Recently, many people, including Huang, Lewis, Morales, Reiner, and Stanton, have enumerated certain factorizations in GLnFq. Much of their results are essentially q-analogues of factorization enumerations coming from Sn in the q-->1 sense. I think this work constitutes a few significant puzzle pieces in an enormous, really difficult puzzle. I will talk about another piece (or fraction of a piece) of this puzzle that I can contribute, which is an enumeration of factorizations of the identity into a product of regular-elliptic elements. Ideally, this is q-analogous to a result of Stanley from the 1981, which enumerates factorizations of the identity into a product of n-cycles. Time permitting, I will talk about my approach and/or the geometry that corresponds to this work.

Fri Nov 02

## Probability Seminar

2:30pm - Vincent Hall 209
Dynamical freezing in a spin glass system with logarithmic correlations
Julian Gold, Northwestern University
##### Abstract:

We consider a continuous time random walk on the two-dimensional discrete torus, whose motion is governed by the discrete Gaussian free field on the corresponding box acting as a potential. More precisely, at any vertex the walk waits an exponentially distributed time with mean given by the exponential of the field and then jumps to one of its neighbors, chosen uniformly at random. We prove that throughout the low-temperature regime and at in-equilibrium timescales, the process admits a scaling limit as a spatial K-process driven by a random trapping landscape, which is explicitly related to the limiting extremal process of the field. Alternatively, the limiting process is a supercritical Liouville Brownian motion with respect to the continuum Gaussian free field on the box. Joint work with Aser Cortines (University of Zurich) and Oren Louidor (Technion).

Fri Nov 02

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Nov 02

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Nov 02

## IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 409
Lecture
Joao Montero, Medtronic
Fri Nov 02

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Topology and combinatorics of the complex of injective words - continuation
Victor Reiner, University of Minnesota
##### Abstract:

I will continue the elementary treatment of properties of this complex, indicating situations where it arises, including a context considered by myself and Peter Webb.

Fri Nov 02

## MathCEP Seminar

10:10am - Vincent Hall 364
MathCEP Seminar

Fri Nov 02

9:30am -
CANCELLED

Thu Nov 01

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
My favorite facts about $\mathrm{GL}_n \mathbb{F}_q$
Graham Gordon, University of Washington
##### Abstract:

Have you ever heard that the symmetric group $\mathfrak{S}_n$ is equal to the finite general linear group $\mathrm{GL}_n \mathbb{F}_q$ in the limit $q \to 1$? This equality casts many mathematical shadows. I will discuss some of my favorites, which involve the (complex) characters of the two groups. I will include a primer on $\mathrm{GL}_n \mathbb{F}_q$ characters, and I will assume some foundational representation theory facts. Next, I will turn the tides and consider the limit $q \to \infty$. Mysteriously, some relationship between $\mathrm{GL}_n \mathbb{F}_q$ and $\mathfrak{S}_n$ as $q \to \infty$ is also casting shadows. Time permitting, I will discuss how character theory can be used to enumerate factorizations in order to segue into tomorrows seminar.

Thu Nov 01

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Nov 01

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Nov 01

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Nov 01

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Nov 01

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
The Stone-von Neumann Theorem
Joe Dickinson, University of Minnesota
##### Abstract:

I plan to talk about some number theoretic implications of the Stone-von Neumann theorem. The Stone-von Neumann theorem is a uniqueness theorem about commutation relations between position and momentum operators. I will give a historical discussion about number theory results implied by Stone-von Neumann.

Thu Nov 01

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Oct 31

## PDE Seminar

3:30pm - Vincent Hall 570
On the global regularity for Einstein-Klein-Gordon coupled system
Alexandru Ionescu, Princeton University
##### Abstract:

I will discuss the Einstein-Klein-Gordon coupled system of General
Relativity, and the problem of global stability of the Minkowski space-time.
This is joint work with Benoit Pausader.

Tue Oct 30

## Dynamical Systems

2:30pm - Ford Hall 130
Dynamical Systems Seminar

Tue Oct 30

## Math Physics Seminar

12:20pm - Vincent Hall 313
Math Physics Seminar

Tue Oct 30

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Oct 30

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Oct 29

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Semigroups and uniqueness arguments for solutions of differential equations in automorphic forms
Amy DeCelles, St. Thomas University
Mon Oct 29

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Preconditioning systems of PDEs: from robust estimates to fast iterations, with applications to simulations of the brain
Ragnar Winther, University of Oslo
##### Abstract:

We will present a set up for simulations of the so-called glymphatic system, which is believed to
be an important mechanism for clearance of waste from the brain. Accumulation of waste can be coupled to
brain shrinkage and conditions like Alzheimers disease. An approach to design mathematical models for the
glymphatic system is to consider the brain as a poroelastic material, with complex geometry, bathed in water, and where various parameters of the model will vary over extreme ranges. A challenge in discretizing such systems in to design methods which behave well with respect variations of the parameters. In particular, we will explain how parameter robust stability estimates for the PDE systems can be used as a key tool to design effective algorithms for the corresponding discrete systems.

Mon Oct 29

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: Symmetric monoidal categories and \Gamma-categories
Amit Sharma, Kent State University
##### Abstract:

A \Gamma-category is a functor from the category of finite based sets and basepoint preserving functions \Gamma^op to Cat. We construct a model category structure on the category of \Gamma-categories, which is symmetric monoidal closed to the Day convolution product. The fibrant objects in this model category structure are those
\Gamma-categories which are often called special \Gamma-categories. The main objective of this research is to establish a Quillen equivalence between a natural model category structure on the category of (small) permutative categories and strict symmetric monoidal functors Perm and our model category structure on \GammaCat. The weak equivalences of the natural model category structure are equivalences of underlying categories. In the paper [1], Segal defined a functor from the category of (small) symmetric monoidal categories into \GammaCat which can be described as a nerve functor for symmetric monoidal categories. The right adjoint \bar{K} of our Quillen equivalence is a thickening of Segal's nerve functor. We construct a permutative category L called Leinster's category, having the universal property that each \Gamma-category extends uniquely to a symmetric monoidal functor along an inclusion functor \Gamma^op > L. The left adjoint L of our Quillen equivalence is a composite functor composed of the symmetric monoidal extension functor indicated above followed by a homtopy colimit functor. In the paper [2], Mandell had shown that Segal's nerve functor (followed by the ordinary nerve functor) induces an equivalence between a homotopy category of Perm, obtained by inverting those strict symmetric monoidal functors which induce a weak homotopy equivalence of simplicial sets upon applying the nerve functor, and a homotopy category of \Gamma-spaces \GammaS obtained by inverting pre-stable equivalences which are those maps of \Gamma-categories which induce a degreewise weak homotopy equivalence of simplicial sets upon applying an E_\infty-completion functor. The objective of Mandell's work is to understand the relation between connective spectra and \Gamma-spaces obtained by applying the Segal's nerve functor to symmetric monoidal categories whereas our objective is to construct a model category of symmetric monoidal categories which is
symmetric monoidal closed.

References:
[1] G. Segal, Categories and cohomology theories, Topology 13 (1974) 293-312.
[2] M. A. Mandell, An Inverse K-theory functor, Doc. Math 15 (2010) 765-791.

Mon Oct 29

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Oct 29

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Lecture
Pratik Chaudhari, University of California, Los Angeles
Mon Oct 29

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Oct 26

## MCFAM Seminar

5:30pm - Vincent Hall 16
Dynamic Linear Models
Katy Micek, 3M Finance
##### Abstract:

Dynamic linear models (DLMs), a subset of state space models, describe the output of a dynamic system as a function of a non-observable state process affected by random errors. Because DLMs can be used either for traditional time series analysis tasks (making inferences on observed states or prediction future observations) or for feature generation in machine learning tasks, they are a very useful tool for any data scientist who works with time series data. As a data scientist on the Data Analytics team for 3M Finance, I work primarily with time series data from the general ledger. Our team both leads data science projects and assists in organizational development of internal capabilities around data science.
In this talk, I will first provide an overview of the Finance organization and describe the technical tasks our team addresses. Next, I will give an introduction on the mathematics of DLMs. Finally, I will conclude showing examples of how DLMs can be used on time series data in a Jupyter notebook demo.

Fri Oct 26

## Algebraic Geometry

3:35pm - Vincent Hall 313
On rigid varieties with projective reduction
Shizhang Li, Columbia University
##### Abstract:

Bosch, Lütkebohmert and Raynaud laid down the foundation relating formal and rigid geometry. The type of questions they treat are mostly concerned with going from the rigid side to formal side. In the past, I considered the opposite type of question, namely to what extent properties on the formal side inform us about rigid geometry. More precisely, we will see what geometric consequences one can deduce under the assumption that the rigid space has a projective reduction. In this talk, I shall first say some background of rigid geometry and Raynaud's theory of formal models along with some examples. Then I will state the main theorem and a corollary. If time permitted, I will say something about the proof.

Fri Oct 26

## Combinatorics Seminar

3:35pm - Vincent Hall 570
High acyclicity of p-subgroup complexes for the symmetric groups
Cihan Bahran, University of Minnesota
##### Abstract:

For any finite group G and a fixed prime p, the topology of the poset of nontrivial elementary abelian p-subgroups contains significant information about the representations of G in characteristic p. For the symmetric group, this poset and its homology remain rather mysterious. A reasonable conjecture is that as we consider larger symmetric groups, the associated posets should get topologically more connected. I will rephrase this conjecture as a representation stability phenomenon ala Church-Ellenberg-Farb, and provide evidence for it by exhibiting high acyclicity of certain subposets.t:

Fri Oct 26

## Probability Seminar

2:30pm - Vincent Hall 209
Some Problems of Robust High-dimensional Statistics
Gilad Lerman, University of Minnesota
##### Abstract:

The talk will first review the problem of robust subspace recovery, which seeks an underlying low-dimensional subspace in a data set that is possibly corrupted with outliers. The emphasis will be on surveying existing theoretical guarantees and tradeoffs. New results for adversarial outliers will also be mentioned. Following this, other related problems will be discussed, along with new results for one of these problems.

Fri Oct 26

## Lie Theory Seminar

2:30pm - Vincent Hall 313
Lie Theory Seminar

Fri Oct 26

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Oct 26

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
Topology and combinatorics of the complex of injective words
Victor Reiner, University of Minnesota
##### Abstract:

According to a result of Farmer, the homology of this complex vanishes except in the bottom and top dimensions. This property is a consequence of shellability of the complex. We will discuss these matters, used in a proof of Nakaoka's theorem on stability of the corestriction map in the group homology of the symmetric groups.

Fri Oct 26

## MathCEP Seminar

10:10am - Vincent Hall 364
The Chicago Guide to Writing about Numbers Book Discussion
Journal Club
##### Abstract:

People who work well with numbers are often stymied by how to write about them. Those who don't often work with numbers have an even tougher time trying to put them into words. For instance, scientists and policy analysts learn to calculate and interpret numbers, but not how to explain them to a general audience. Students learn about gathering data and using statistical techniques, but not how to write about their results. And readers struggling to make sense of numerical information are often left confused by poor explanations. Jane Miller, an experienced research methods and statistics teacher, gives writers the assistance they need. The Chicago Guide to Writing about Numbers helps bridge the gap between good quantitative analysis and good expository writing. Field-tested with students and professionals alike, this book shows writers how to think about numbers during the writing process. By providing basic guidelines for successfully using numbers in prose, The Chicago Guide to Writing about Numbers will help writers of all kinds clearly and effectively tell a story with numbers as evidence.

Fri Oct 26

9:30am -
CANCELLED

Thu Oct 25

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra Seminar

Thu Oct 25

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Oct 25

## Algebraic Geometry

1:25pm - Vincent Hall 313
An example of liftings with different Hodge numbers
Shizhang Li, Columbia University
##### Abstract:

Does a smooth proper variety in positive characteristic know the Hodge numbers of its liftings? The answer is "of course not". However, it's not that easy to come up with a counter-example. In this talk, I will first introduce the background of this problem. Then I shall discuss some obvious constraints of constructing a counter-example. Lastly I will present such a counter-example and state a few questions of similar flavor for which I do not know an answer.

Thu Oct 25

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Oct 25

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Commutative Algebra Seminar

Thu Oct 25

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Oct 25

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Cryptographic Multilinear Maps from Elliptic Curves
Mahrud Sayrafi, University of Minnesota
##### Abstract:

We will begin with defining cryptographic multilinear maps, briefly discussing some of their applications, and referencing one such map from Boneh-Silverberg '03. After that, we will extend a problem involving isogenies of elliptic curves into an open problem of finding cryptographic invariant maps from Boneh, et al. '18.stract:

Thu Oct 25

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Oct 24

## PDE Seminar

3:30pm - Vincent Hall 570
PDE Seminar

Tue Oct 23

## Dynamical Systems

2:30pm - Ford Hall 130
Snaking in the Swift-Hohenberg Equation in Dimension 1+Epsilon
Jason Bramburger, Brown University
##### Abstract:

The Swift-Hohenberg equation is a widely studied partial differential equation which is known to support a variety of spatially localized structures. The one-dimensional equation exhibits spatially localized steady-state solutions which give way to a bifurcation structure known as snaking. That is, these solutions bounce between two different values of the bifurcation parameter while ascending in norm. The mechanism that drives snaking in one spatial dimension is now well-understood, but recent numerical investigations indicate that upon moving to two spatial dimensions, the related radially-symmetric spatially-localized solutions take on a significantly different snaking structure which consists of three major components. To understand this transition we apply a dimensional perturbation in an effort to use well-developed methods of perturbation theory and dynamical systems. In particular, we are able to identify key characteristics that lead to the segmentation of the snaking branch and therefore provide insight into how the bifurcation structure changes with the spatial dimension.

Tue Oct 23

## Math Physics Seminar

12:20pm - Vincent Hall 313
Math Physics Seminar

Tue Oct 23

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Oct 23

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Oct 22

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Automorphic Hamiltonians
Adrienne Sands, University of Minnesota
##### Abstract:

We apply methods of quantum mechanics to construct self-adjoint, purely discrete pseudo-differential operators which characterize a nuclear Frechet Schwartz space of automorphic forms.

Mon Oct 22

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Applied and Computational Math Colloquium

Mon Oct 22

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: Finitely generated sequences of linear subspace arrangements
Nir Gadish, University of Chicago
##### Abstract:

Hyperplane arrangements are a classical meeting point of topology, combinatorics and representation theory. Generalizing to arrangements of linear subspaces of arbitrary codimension, the theory becomes much more complicated. However, a crucial observation is that many natural sequences of arrangements seem to be defined using a finite amount of data.

In this talk I will describe a notion of 'finitely generation' for collections of arrangements, unifying the treatment of known examples. Such collections turn out to exhibit strong forms of stability, both in their combinatorics and in their cohomology representation. This structure makes the appearance of representation stability transparent and opens the door to generalizations.

Mon Oct 22

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Oct 22

## IMA Data Science Lab Seminar

1:25pm - Lind 409
Large Sample Asymptotics of Graph-based Methods in Machine Learning: Mathematical Analysis and Implications
Nicolas Garcia-Trillos, University of Wisconsin, Madison
##### Abstract:

Many machine learning procedures aimed to extract information from data can be defined as precise mathematical objects that are constructed in terms of the data. It is often assumed that the data is big in complexity but also in quantity, and in this large amount of data setting, a basic mathematical concept that one can explore is that of closure of a given class of statistical procedures (i.e. what are the limiting procedures as the number of data points available goes to infinity.) In this talk, I will explore this notion in the context of graph-based methods. Examples of such methods include minimization of Cheeger cuts, spectral clustering, and graph-based bayesian semi-supervised learning, among others. I will introduce some of the mathematical ideas needed for the analysis, as well as show some of the implications of it: our results show statistical consistency of the methods, provide with quantitative information in the form of scaling of parameters and rates of convergence, imply qualitative properties at the discrete level, and suggest the use of appropriate algorithms.

Mon Oct 22

## Cockburn's Seminar

9:00am - Vincent Hall 301
Cockburn's Seminar

Fri Oct 19

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Oct 19

## Lie Theory Seminar

4:30pm - Vincent Hall 313
On Several Classical Number Theory Problems
Tianxin Cai, Zhejiang University and University of Iowa
Fri Oct 19

## Combinatorics Seminar

3:35pm - Vincent Hall 570
Optimal switching sequence for switched linear systems
Qie He, UMN
##### Abstract:

We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of n-by-n real matrices and an n-dimensional real vector, find a sequence of K matrices, each chosen from the given set of matrices, to maximize a convex function over the product of the K matrices and the given vector. This simple problem has many applications in operations research and control, yet a moderate-sized instance is challenging to solve to optimality for state-of-the-art optimization software. We propose a simple exact algorithm for this problem. The efficiency of our algorithm depends heavily on whether the given set of matrices has the oligo-vertex property, a concept we introduce for a finite set of matrices. The oligo-vertex property captures how the numbers of extreme points for a sequence of K convex polytopes related to the given matrices grow with respect to K. We derive several sufficient conditions for a set of matrices to have this property, and pose several open questions related to this property.

Fri Oct 19

## Probability Seminar

2:30pm - Vincent Hall 209
Probability Seminar

Fri Oct 19

## Differential Geometry and Symplectic Topology Seminar

2:30pm - Vincent Hall 6
The Smooth 4-dimensional Poincare Conjecture and Dehn surgery on links
Alex Zupan, University of Nebraska
##### Abstract:

The smooth version of the 4-dimensional Poincare Conjecture (S4PC) states that every homotopy 4-sphere is diffeomorphic to the standard 4-sphere. One way to attack the S4PC is to examine a restricted class of 4-manifolds. For example, Gabai's proof of Property R implies that every homotopy 4-sphere built with one 2-handle and one 3-handle is standard. In this talk, we consider homotopy 4-spheres X built with two 2-handles and two 3-handles, which are uniquely determined by the attaching link L for the 2-handles in the 3-sphere. We prove that if one of the components of L is the connected sum of a torus knot T(p,2) and its mirror (a generalized square knot), then X is diffeomorphic to the standard 4-sphere. This is joint work with Jeffrey Meier.

Fri Oct 19

## Student Topology Seminar

1:30pm - Vincent Hall 311
Student Algebra and Topology Seminar

Fri Oct 19

## Algebraic Representation Theory Seminar

1:25pm - Vincent Hall 206
A theorem of Nakaoka on the homology of symmetric groups - continuation
Peter Webb, University of Minnesota
##### Abstract:

A theorem of Nakaoka states that the inclusion of symmetric groups induces an isomorphism of group homology provided that the degrees of the symmetric groups are large enough. This week I will continue with the proof of this, explaining the equivariant cohomology spectral sequence and the specific calculations that arise, trying to assume as little as I can.

Fri Oct 19

## MathCEP Seminar

10:10am - Vincent Hall 364
MathCEP Seminar

Fri Oct 19

9:30am -
CANCELLED

Thu Oct 18

## Student Combinatorics Seminar

4:40pm - Vincent Hall 570
Student Combinatorics and Algebra Seminar

Thu Oct 18

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Oct 18

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry / Symplectic Topology Seminar

Thu Oct 18

## Commutative Algebra Seminar

1:25pm - Ford Hall 170
Computations in Local Rings using Macaulay2
Mahrud Sayrafi, University of Minnesota
##### Abstract:

Local rings are ubiquitous in commutative algebra and algebraic geometry. In this talk I will describe two avenues for computing in local rings with respect to prime ideals, first using the associated graded algebra and then using only Nakayama's lemma. Time permitting, I will demonstrate various examples and applications, such as computing the Hilbert-Samuel multiplicity, using Macaulay2.

Thu Oct 18

## Math Club Seminar

12:20pm - Vincent Hall 570
Math Club Seminar

Thu Oct 18

## Student Number Theory Seminar

12:20pm - Vincent Hall 313
Elliptic functions and elliptic curves in the 19th century
Devadatta Hegde, University of Minnesota
##### Abstract:

We will give an account of the work on Weierstrass and Jacobi proving a result due to Abel on meromorphic functions on the torus. These are results about complex points of elliptic curves which suggest attributes for rational points. These examples were later greatly extended at the hands of several mathematicians and reached a high-point with the GAGA principle by Serre. It's also the first example of a Riemann-Roch type theorem which were greatly extended by Grothendieck, Atiyah and Singer. Only some familiarity with Cauchy's theorem in complex analysis is needed to understand the talk.

Thu Oct 18

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Wed Oct 17

## PDE Seminar

3:30pm - Vincent Hall 570
Continuum Limits of Semi-Supervised Learning on Graphs
Matthew Thorpe, University of Cambridge
##### Abstract:

Given a data set $\{x_i\}_{i=1}^n$ with labels $\{y_i\}_{i=1}^N$ on the first $N$ data points the goal of semi-supervised is to infer labels on the remaining $\{x_i\}_{i=N+1}^n$ data points. In this talk we use a random geometric graph model with connection radius $r(n)$. The framework is to consider objective functions which reward the regularity of the estimator function and impose or reward the agreement with the training data, more specifically we will consider discrete p-Laplacian and fractional Laplacian regularization.

The talk concerns the asymptotic behaviour in the limit where the number of unlabelled points increases while the number of training points remains fixed. The results are to uncover a delicate interplay between the regularizing nature of the functionals considered and the nonlocality inherent to the graph constructions. I will give almost optimal ranges on the scaling of $r(n)$ for asymptotic consistency to hold. Furthermore, I will setup the Bayesian interpretation of this problem.

This is joint work with Matt Dunlop (Caltech), Dejan Slepcev (CMU) and
Andrew Stuart (Caltech).

Mathew Thorpe is a Research Fellow at the Cantab Capital Institute for the Mathematics of Information, Department of Applied Mathematics and Theoretical Physics, University of Cambridge.

.

Tue Oct 16

## Dynamical Systems

2:30pm - Ford Hall 130
Run-and-tumble clusters: blowing up the blowup
Arnd Scheel
##### Abstract:

Motivated by patterns in colonies of myxobacteria, I will show some results on clustering in run-and-tumble processes. We look at two populations of agents on the real line, propagating with speed 1 to the left or to the right, respectively. They tumble, that is, reverse direction, with a rate that depends on encounters with agents traveling in the opposite direction in a nonlinear fashion. I will show some phenomena and then explain how elementary dynamical systems methods can help understanding the formation of localized clusters in the population. The talk should be accessible to graduate students with basic knowledge in dynamical systems

Tue Oct 16

## Math Physics Seminar

12:20pm - Vincent Hall 313
Math Physics Seminar

Tue Oct 16

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar

Tue Oct 16

## Climate Seminar

11:15am - 570 Vincent Hall
Climate Change Seminar
Richard McGehee
Mon Oct 15

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 1
Automorphic Hamiltonians
Adrienne Sands, University of Minnesota
##### Abstract:

We apply methods in quantum mechanics to construct self-adjoint, purely discrete pseudo-differential operators which characterize a nuclear Fréchet Schwartz space of automorphic forms"

Mon Oct 15

## Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Modeling gas, fluid, and particle transport in the lung airway system: the curse of scales
Marcel Filoche, Ecole Polytechnique, Paris
##### Abstract:

The pulmonary airway system is a highly hierarchical tree-like 3D network in charge of transferring oxygen from the upper airways down to the alveolar region where the gas exchange occurs between air and blood. It is also the place of numerous particle and fluid transport processes. Given the complexity of the anatomy and of the physics involved, numerical simulation is a remarkable tool for investigating the properties of this organ seen as a "transport system", understanding its behavior and possible failures, and predicting the outcome of therapies. However, the range of scales represents here a huge challenge: from the meter scale of the entire organ size down to the micron scale of the mucus layer, about 5 to 6 orders of magnitude of length scale are crossed.

In this talk, we will present several examples of numerical models able to capture the various aspects of the lung airway system, from the simplest linear approach of gas transport to more advanced computational fluid dynamics simulation. We will show, in particular, how the range of scales involved and the difficulty to access the actual parameters in the patient imposes to use a hierarchy of models and a diversity of numerical techniques. We will explain how these models can be used either to reach a general understanding of the system or to design patient specific diagnosis and therapy.

Mon Oct 15

## Topology Seminar

3:30pm - Vincent Hall 301
Topology Seminar: Rigidity of warped cones and coarse geometry of expanders
Wouter van Limbeek, UIC
##### Abstract:

Finitely generated subgroups of compact Lie groups give rise to expander graphs via a warped cone construction. We study the dependence of the coarse geometry of such expander graphs on the original subgroup and establish a dynamical analogue of quasi-isometric rigidity theorems in geometric group theory: Namely, the coarse geometry of the warped cone determines the subgroup up to commensurability, unless the group has abelian factors. This is joint work with David Fisher and Thang Nguyen.

Mon Oct 15

## Dynamical Systems

2:30pm - Vinent Hall 570
Dynamical Systems Seminar

Mon Oct 15

## IMA Data Science Lab Seminar

1:25pm - Keller 3-180
Lecture
Raj Nadakuditi, University of Michigan