# Past Seminars

Automorphic Forms & Number Theory [will not meet]

Cockburn's Seminar

State of Health Economy as we Transition to a new Administration

##### Abstract:

Professor Steve Parente will talk about the long arc of health reform in the United States and the choices that are now being considered for the the next chapter. He will present results for a health reform microsimulation model to highlight the results of those choices on the uninsured in the US, premiums paid and federal budget implications.

Reading Seminar on Harmonic Analysis

Set-Valued Skyline

##### Abstract:

Set-valued tableaux play an important role in combinatorial K-theory. Separately, semistandard skyline fillings are a combinatorial model for Demazure atoms and key polynomials. We unify these two concepts by defining a set-valued extension of semistandard skyline fillings and then give analogues of results of J. Haglund, K. Luoto, S. Mason, and S. van Willigenberg.

Applied and Computational Math Colloquium

The limiting density of the positive spins for majority dynamics on 3-regular tree has no jumps

##### Abstract:

We consider the majority dynamics on the infinite 3-regular tree, where each vertex has an i.i.d. Poisson clock attached to it, and when the clock of a vertex rings, the vertex looks at the spins of its three neighbors and flips its spin, if necessary, to come into agreement with majority of its neighbors. The initial spins of the vertices are taken to be i.i.d. Bernoulli random variables with parameter p. We show that the probability that the limiting spin at the root is + is continuous with respect to the initial bias p. Our argument relies upon mass transport principle. The talk is based on an ongoing work with M. Damron.

Math Physics Seminar

Student Combinatorics Seminar

Colloquium

Lagrangian-type Submanifolds of G2 and Spin(7) Manifolds

##### Abstract:

The study of Lagrangian submanifolds has played a fundamental role in furthering the field of symplectic geometry. Lagrangian submanifolds reveal information about Hamiltonian mechanics, symplectic rigidity, and local invariants of symplectic manifolds. Further, a deeper understanding of Lagrangian submanifolds has provided insight towards establishing a correspondence between Calabi-Yau mirror pairs in Kontsevich's homological mirror symmetry via the Fukaya category. In this talk, we discuss the analogues for Lagrangian submanifolds in G2 and Spin(7) geometry. We will discuss properties of these submanifolds as well as their deformation spaces. This is joint work with Sema Salur.

Student Number Theory Seminar

Welcome Week

Commutative Algebra Seminar

Recursive Integral Eigenvalue Solver with Cayley Transformation

##### Abstract:

Recently, a non-classical eigenvalue solver, called {\bf RIM}, was proposed to compute (all) eigenvalues in a region on the complex plane. Without solving any eigenvalue problems, it tests if a region contains eigenvalues using an approximate spectral projection. Regions that contain eigenvalues are subdivided and tested recursively until eigenvalues are isolated with a specified precision. This makes {\bf RIM} an eigenvalue solver distinct from all existing methods. Furthermore, it requires no a priori spectral information. In this talk, we implement an improved version of {\bf RIM} for non-Hermitian eigenvalue problems. Using Cayley transforms, the computation cost is reduced significantly also it inherits all the advantages of RIM. Numerical examples are presented and compared with 'eigs' in Matlab.

Convexity of Level Sets and a Two-point Function

Reading Seminar for Automorphic Forms

A Free Boundary Problem on Cones

##### Abstract:

The one phase free boundary problem shares a well-known connection to area-minimizing surfaces. In this talk we review this connection and then discuss the one-phase problem on rough surfaces, and in particular cones. After reviewing results of the author with Chang Lara for the one-phase problem on two-dimensional cones, we revisit the connection to area-minimizing surfaces to gain insight into the problem on higher dimensional cones. We then present new results on when the free boundary is allowed to pass through the vertex of a three-dimensional cone as well as results for higher dimensional cones.

Student Algebraic Topology Seminar

Algebraic Geometry Seminar

New methods in free boundary problems

##### Abstract:

In this talk we will give an introduction to the area of free boundary problems. We will discuss some of the inherent difficulties in studying free boundary problems. After reviewing classical techniques and their limitations, we will discuss new techniques that have emerged over the past couple of years (some in the past couple of months) to solve open problems. We will conclude by discussing various open problems and future directions in free boundary problems.

Lie Theory Seminar

Analysis and PDE Working Seminar

Colloquium

Colloquium

Diferential Geometry and Symplectic Topology Seminar

“Big Data” in Image Analysis

##### Abstract:

Image analysis is the quantitative analysis of images. It feeds on advances in mathematics, signal processing and machine learning to apply them to information extraction from images, N-dimensional sampled signals. In this talk we will attempt to explore applications of mathematics to different areas of image analysis, from acquisition, to processing, to data exploration. We will see how advances in sensing equipment creates additional challenges for processing and extracting scientific insights.

Thomas obtained his BSc and MSc in Computer Engineering at Politecnico di Milano in 2005. His PhD was defended in 2010 at the University of Navarra, with the title "Automation of Early Lung Cancer Detection", a work he developed at the Center for Applied Medical Research in Pamplona. During his Ph.D. he was a visiting scientist at the CBIA in Brno and at Sudar Lab in the Lawrence Berkeley National Laboratory. After a two years postdoc at the Ecole Polytechnique Federale de Lausanne working on the analysis of super-resolution microscopy images at the LEB he worked as an image analyst at the Center for Genomic Regulation in Barcelona in the Advanced Light Microscopy Unit and in the laboratory of Luis Serrano, before moving to the U of M.

Climate Change Seminar - NOT MEETING

[will not meet]

Cockburn's Seminar

Wave phenomena in metamaterials and photonic crystals

##### Abstract:

Metamaterials are materials whose electromagnetic or acoustic

properties are controlled by their internal structure. Typically these

structures can be periodic and the period or characteristic length scale

of the internal structure is much smaller than the wavelength. A familiar

example is red stained glass made from sub wavelength gold nanoparticles.

On the other hand when the period of the internal structure is on the same

length scale as the wavelength then destructive interference can occur.

This gives rise to frequency intervals where no waves can propagate inside

the material. These are the well known photonic band gap crystals and

their effects can be seen in the coloration of butterfly wings. In this

lecture we provide a brief history of metamaterials and photonic band gap

crystals and provide an overview of the mathematical modeling. We

highlight auxiliary spectral problems directly related to the physical

structure of these materials. We illustrate how these spectra can be used

as tools in the design of both metamaterials and photonic band gap

crystals. This is joint work with Yue Chen and Robert Viator.

Model Validation

##### Abstract:

The presentation will focus on model validation’s role within a model risk management framework. Applications of model validation concepts to the loss forecasting methodologies and the CCAR exercise will be discussed.

Dr. West's Bio: https://www.linkedin.com/in/james-west-bb027474

Lyashko-Looijenga Morphisms and Geometric Factorizations of a Coxeter Element

##### Abstract:

A common theme in Combinatorics is an unconditional love for the symmetric group. We like to investigate structural and numerological properties of various objects associated with it. It often happens that such objects and phenomena can be generalized to the other (complex) reflection groups as well.

A problem that goes back to Hurwitz and the 19th century is to enumerate (reduced) factorizations of the long cycle (12..n)? Sn? into factors from prescribed conjugacy classes. In the reflection groups case, it corresponds to enumerating factorizations of a Coxeter element.

Bessis gave a beautiful geometric interpretation of such factorizations by using a variant of the Lyashko-Looijenga (LL) map, a finite morphism coming from Singularity theory. We extend some of Bessis' and Ripoll's work and use the LL map to enumerate the so called "primitive factorizations" of a Coxeter element c. That is, factorizations of the form c=w? t1? tk?, where w? belongs to a prescribed conjugacy class and the ti?'s are reflections.

Reading Seminar on Harmonic Analysis

Ground state energy and energy landscape of the spherical mixed p-spin model

##### Abstract:

Spin glasses are disordered spin systems originated from the desire of understanding the strange magnetic behavior of certain alloys in physics. In this talk, we will focus on the landscape of the spherical mixed p-spin model. First, we will present the Crisanti-Sommers formula for the ground state energy. Second, we will discuss some geometric properties of the energy landscape corresponding to different mixtures. Based on joint works with A. Auffinger and A. Sen.

Applied and Computational Math Colloquium

3-body problem: quantum ground state, classical planar dynamics

##### Abstract:

The quantum and classical dynamics of a $3$-body system with equal masses

in $d$-dimensional space with interaction depending only on mutual

(relative) distances.

The study is restricted to solutions in the space of relative motion which

are functions of mutual (relative) distances only.

It is shown that these solutions correspond to motion of 3-dimensional

particle in curved space with remarkable metric. (Quasi)-exactly-solvable

Schroedinger operators in this curved space are found.

Student Combinatorics Seminar

Colloquium

Diferential Geometry and Symplectic Topology Seminar

Student Number Theory Seminar

Welcome Week

Commutative Algebra Seminar

Poisson equation on complete manifolds: applications to steady Ricci solitons

Reading Seminar for Automorphic Forms

PDE Seminar

Algebraic Geometry Seminar

Student Algebraic Topology Seminar

Lie Theory Seminar

Realtime fluid simulation in the Google Chrome Web Browser

##### Abstract:

The rise of web browsers (e.g. Chrome, Safari, Firefox) that support GPU-accelerated graphics (WebGL) has opened the floodgates (no pun intended) for realtime fluid solvers on the web. Useful for visual effects and education, what was previously only possible as a downloadable executable can now be written as a simple web page. Based off a highly cited article in Nvidia's famous "GPU Gems" collection of papers, I will discuss the general mathematical and numerical framework for realtime fluid simulation in the web browser. The talk will be mostly computational, but the numerical techniques employed give a unique perspective on the structure of the Navier-Stokes equation and a cool demo of a new frontier for accessible realtime visualization.

Colloquium

Colloquium

Diferential Geometry and Symplectic Topology Seminar

Climate Change Seminar

Invariant Dirac operators on G/K, III

Cockburn's Seminar

MFM Student Seminar - A Student’s Crash Course on Quantitative Trading: Part 2

##### Abstract:

This talk is the second of a two-part lecture series on the field of quantitative trading that addresses the gap: what should students know about the field in order to be able to discuss their interest with industry professionals? We will discuss the typical recruiting schedule, how to network your way into an interview opportunity, and how interviews are typically structured between different kinds of firms.

Reading Seminar on Harmonic Analysis

Ehrhart Theory for spanning lattice polytopes

##### Abstract:

Ehrhart Theory is the study of lattice points in polytopes. The central object of study is the Ehrhart series of a lattice polytope P, which is the generating function for the number of lattice points in the various dilations of P. It is a rational function, and the coefficients of its numerator polynomial are known as the h^*-vector of P. Our main result is that if the lattice points in P affinely span the ambient lattice, then the h^*-vector has no inner zeros. This generalizes a recent theorem by Blekherman, Smith, and Velasco, and implies a polyhedral consequence of the Eisenbud-Goto conjecture.

This is joint work with Benjamin Nill and Johannes Hofscheier.

Applied and Computational Math Colloquium

Probability Seminar

Startups and Machine Learning in the Wild

##### Abstract:

Many of the problems that you will face when applying AI in the business world are not algorithmic. This talk will draw from a variety applied machine learning scenarios that we have encountered at Deep Machine and talk about the types of problems to expect, the reasons that businesses care and some of the trade offs that we face as a small company in a big data world. It will address the breadth of work being done and discuss some of the tradeoffs between startup and big company data science.

Josh Cutler is currently the CEO and Founder of Deep Machine. He holds a BS degree in computer science and math from UW-Madison and later pursued a PhD at Duke University, where he built predictive models analyzing international conflict. He began his career commercializing research at Microsoft Live Labs. He has subsequently served in leadership roles at multiple data-focused startups, and founded and led a company to acquisition.

Math Physics Seminar

Student Combinatorics Seminar

Colloquium

Some Recent Progress of the Uniformization Conjecture

##### Abstract:

Yau's uniformization conjecture states that a complete nonimpact Kahler manifold with positive bisectional curvature is biholomorphic to the complex Euclidean space. We survey some recent progress of this conjecture by using the Gromov-Hausdorff convergence theory. Also, we discuss some applications to noncompact Ricci flat Kahler manifolds.

Student Number Theory Seminar

Welcome Week

Commutative Algebra Seminar

Tutorial: 2D materials polaritons

##### Abstract:

In recent years, enhanced light-matter interactions through a plethora of dipole-type polaritonic excitations have been observed in two-dimensional (2D) layered materials. In graphene, electrically tunable and highly confined plasmon-polaritons were predicted and observed, opening up opportunities for optoelectronics, bio-sensing and other mid-infrared applications. In hexagonal boron nitride, low-loss infrared-active phonon-polaritons exhibit hyperbolic behavior for some frequencies, allowing for ray-like propagation exhibiting high quality factors and hyperlensing effects. In transition metal dichalcogenides, reduced screening in the 2D limit leads to optically prominent excitons with large binding energy, with these polaritonic modes having been recently observed with scanning near field optical microscopy. Here, we review recent progress in state-of- the-art experiments, survey the vast library of polaritonic modes in 2D materials, their optical spectral properties, figures-of- merit and application space. Taken together, the emerging field of 2D material polaritonics and their hybrids provide enticing avenues for manipulating light-matter interactions across the visible, infrared to terahertz spectral ranges, with new optical control beyond what can be achieved using traditional bulk materials. These tutorials will provide an introduction and overview of research in this field.

[1] Low T, Chaves A, Caldwell JD, Kumar A, Fang NX, Avouris P, Heinz TF, Guinea F, Martin-Moreno L, Koppens F. Polaritons in layered two-dimensional materials. Nature Materials. 2016 Nov 28.

Poisson Equation on Complete Manifolds

Reading Seminar for Automorphic Forms

PDE Seminar

Algebraic Geometry Seminar

Student Algebraic Topology Seminar

Tutorial: 2D materials polaritons

##### Abstract:

In recent years, enhanced light-matter interactions through a plethora of dipole-type polaritonic excitations have been observed in two-dimensional (2D) layered materials. In graphene, electrically tunable and highly confined plasmon-polaritons were predicted and observed, opening up opportunities for optoelectronics, bio-sensing and other mid-infrared applications. In hexagonal boron nitride, low-loss infrared-active phonon-polaritons exhibit hyperbolic behavior for some frequencies, allowing for ray-like propagation exhibiting high quality factors and hyperlensing effects. In transition metal dichalcogenides, reduced screening in the 2D limit leads to optically prominent excitons with large binding energy, with these polaritonic modes having been recently observed with scanning near field optical microscopy. Here, we review recent progress in state-of- the-art experiments, survey the vast library of polaritonic modes in 2D materials, their optical spectral properties, figures-of- merit and application space. Taken together, the emerging field of 2D material polaritonics and their hybrids provide enticing avenues for manipulating light-matter interactions across the visible, infrared to terahertz spectral ranges, with new optical control beyond what can be achieved using traditional bulk materials. These tutorials will provide an introduction and overview of research in this field.

[1] Low T, Chaves A, Caldwell JD, Kumar A, Fang NX, Avouris P, Heinz TF, Guinea F, Martin-Moreno L, Koppens F. Polaritons in layered two-dimensional materials. Nature Materials. 2016 Nov 28.

Lie Theory Seminar

Partial regularity of harmonic maps into spheres

##### Abstract:

We will introduce the notion of harmonic maps and discuss the results of Evans on partial regularity of harmonic maps into spheres.

Colloquium

Colloquium

Dictionary Design for Graph Signal Processing

##### Abstract:

By transforming data into a new domain, techniques from statistics and signal processing such as principle components analysis and Fourier, wavelet, time-frequency, and curvelet transforms can sparsely represent and reveal relevant structural properties of time series, audio signals, images, and other data that live on regular Euclidean spaces. Such transform methods prove useful in compression, denoising, inpainting, pattern recognition, classification, and other signal processing and machine learning tasks. Unfortunately, naively applying these “classical” techniques to data on graphs would ignore key dependencies arising from irregularities in the graph data domain, and result in less informative and less sparse representations of the data. A key challenge in graph signal processing is therefore to incorporate the graph structure of the underlying data domain into dictionary designs, while still leveraging intuition from classical computational harmonic analysis techniques. In this talk, I will motivate the dictionary design problem for graph signals, examine some recently proposed dictionaries for graph signals, and discuss open issues and challenges.

David Shuman received the B.A. degree in economics and the M.S. degree in engineering-economic systems and operations research from Stanford University, Stanford, CA, USA, in 2001 and the M.S. degree in electrical engineering: systems, the M.S. degree in applied mathematics, and the Ph.D. degree in electrical engineering: systems from the University of Michigan, Ann Arbor, USA, in 2006, 2009, and 2010, respectively. He joined the Department of Mathematics, Statistics, and Computer Science, Macalester College, St. Paul, MN, USA, as an Assistant Professor in January 2014. From 2010 to 2013, he was a Postdoctoral Researcher at the Institute of Electrical Engineering, Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland. His research interests include signal processing on graphs, computational harmonic analysis, and stochastic scheduling and resource allocation problems.

Diferential Geometry and Symplectic Topology Seminar

Climate Change Seminar - NO MEETING THIS WEEK

Tutorial: 2D materials polaritons

##### Abstract:

In recent years, enhanced light-matter interactions through a plethora of dipole-type polaritonic excitations have been observed in two-dimensional (2D) layered materials. In graphene, electrically tunable and highly confined plasmon-polaritons were predicted and observed, opening up opportunities for optoelectronics, bio-sensing and other mid-infrared applications. In hexagonal boron nitride, low-loss infrared-active phonon-polaritons exhibit hyperbolic behavior for some frequencies, allowing for ray-like propagation exhibiting high quality factors and hyperlensing effects. In transition metal dichalcogenides, reduced screening in the 2D limit leads to optically prominent excitons with large binding energy, with these polaritonic modes having been recently observed with scanning near field optical microscopy. Here, we review recent progress in state-of- the-art experiments, survey the vast library of polaritonic modes in 2D materials, their optical spectral properties, figures-of- merit and application space. Taken together, the emerging field of 2D material polaritonics and their hybrids provide enticing avenues for manipulating light-matter interactions across the visible, infrared to terahertz spectral ranges, with new optical control beyond what can be achieved using traditional bulk materials. These tutorials will provide an introduction and overview of research in this field.

[1] Low T, Chaves A, Caldwell JD, Kumar A, Fang NX, Avouris P, Heinz TF, Guinea F, Martin-Moreno L, Koppens F. Polaritons in layered two-dimensional materials. Nature Materials. 2016 Nov 28.

Invariant Dirac operators II

Cockburn's Seminar

MFM Student Seminar - A Student’s Crash Course on Quantitative Trading: Part 1

##### Abstract:

This talk is the first of a two-part lecture series on the field of quantitative trading that addresses the gap: What should students know about the field in order to be able to discuss their interest with industry professionals? We will discuss the infrastructure of electronic exchanges, the distinction between buy-side and sell-side traders, the different types of trading firms, and the trading strategies that characterize these firms.

Bio: https://www.linkedin.com/in/keenangao

Dimer models on cylinders over Dynkin diagrams

##### Abstract:

Let G be a Lie group of type ADE and P be a parabolic subgroup. It is known that there exists a cluster structure on the coordinate ring of the partial flag variety G/P (see the work of Geiss, Leclerc, and Schroer). Since then there has been a great deal of activity towards categorifying these cluster algebras. Jensen, King, and Su gave a direct categorification of the cluster structure on the homogeneous coordinate ring for Grassmannians (that is, when G is of type A and P is a maximal parabolic subgroup). In this setting, Baur, King, and Marsh gave an interpretation of this categorification in terms of dimer models. In this talk, I will give an analog of dimer models for groups in other types by introducing a technique called “constructing cylinders over Dynkin diagrams”, which can (conjecturally) be used to generalize the result of Baur, King, and Marsh.

The Limit Shape of Convex Peeling

##### Abstract:

Convex peeling is an algorithm for arranging a set of points in Euclidean space into layers by repeatedly removing the vertices of the convex hull. We show that the convex peeling of random points has a large sample size continuum limit that corresponds to solving a degenerate elliptic PDE in the viscosity sense. This is joint work with Charles K. Smart (University of Chicago).

Applied and Computational Math Colloquium

Math Physics Seminar

A Sheaf Theoretic Modeling and Composition Framework for Complex Systems of Systems: Application to the Traffic Collision Avoidance

##### Abstract:

The growing need and requirement of today's systems is to provide a multitude of services improving the performance of the processes they monitor and control. To achieve a scalable design paradigm most of these systems are developed by first designing, analyzing and testing subsystems and then by interconnecting them. In order to achieve scalability without completely sacrificing analytical guarantees one needs to mathematically formalize the composition operation. One of the key characteristics such a framework needs to have is the ability to easily compose different models of computation. These are conveniently used to design and analyze each subsystem, but such model may become extremely inconvenient at the time of the composition. This means that the designer needs to first choose a common abstraction model and then translate each submodel in order to compose. Contract-based design methodologies tend to be more flexible in this context, given that no explicit model of each subsystem is required and only certain 'assume-guarantee' contracts are defined. However, again, the mathematical formalization of each subcontract might be easily expressed using different formalisms, making the characterization of the contract of the composition difficult to describe.

In this talk we introduce a new framework for modeling and composing system of systems. The framework enables us to translate various mathematical submodels into a common abstraction based on interval sheaves. Leveraging the compositionality properties of sheaves we are able to define abstract machines that can be composed in an arbitrary way with strong mathematical guarantees. We introduce this framework and then show its applicability to an aerospace scenario. While the example is fairly simple, the purpose is to highlight the capability of the sheaf-based abstraction to enable composition of subsystems that are inherently described by different models of computation.

Joint work with Dr. David Spivak (MIT) and Srivatsan Varadarajan (Honeywell)

Alberto Speranzon received the ‘‘Laurea’’ degree in computer engineering from University of Padova, Italy in 2000, and a Ph.D. in automatic control from the School of Electrical Engineering, Royal Institute of Technology (KTH), Stockholm, Sweden in 2006. In September 2015 he joined Honeywell Labs in Minneapolis, MN, USA where he is a research scientist. At Honeywell, Alberto is working on autonomous systems, leading such research area as program mana

Student Combinatorics Seminar

Colloquium

Diferential Geometry and Symplectic Topology Seminar

Welcome Week

Student Number Theory Seminar

Commutative Algebra Seminar

A Gap Theorem for Gradient Ricci Shrinkers of Dimension Four

##### Abstract:

We will talk about the recent result of Y. Li and B. Wang (https://arxiv.org/abs/1701.01989), which shows that nontrivial flat cones cannot be approximated by smooth Ricci shrinkers with bounded scalar curvature in dimension 4.

Planar propagating terraces and the dynamics of front-like solutions of parabolic equations

##### Abstract:

We consider bounded front-like solutions of parabolic equations $u_t=\Delta u+f(u)$ on $\mathbb R^N$. Front-like solutions are solutions with initial data $u_0(x_1,x_2,\dots,x_N)$ whose limits as $x_1\to\pm\infty$ exist, uniformly in $(x_2,\dots,x_N)$, and are equal to distinct zeros of $f$. If $N=1$, we show a general result on the approach of front-like solutions to propagating terraces, or, stacked families of traveling fronts. For $N\ge 2$, we use the propagating terraces of the one-dimensional problem, or, planar propagating terraces, to show the asymptotic one-dimensional symmetry of front-like solutions and related results.

Algebraic Geometry Seminar

Student Algebraic Topology Seminar

Colloquium

Analysis and PDE Working Seminar

Colloquium

Diferential Geometry and Symplectic Topology Seminar

Climate Change Seminar

Invariant Dirac operators on G/K

Cockburn's Seminar

Automorphic Forms and Number Theory

##### Abstract:

tba

MCFAM Seminar - No Seminar

Old Problems on Multiplicities and New Families of Tableaux

##### Abstract:

Computing weight multiplicities of dominant weight of highest weight modules over finite simple Lie algebra is quite old problem. Weyl's character formula and Freudenthal's formula give a way to compute such weight multiplicities, which looks not so practical. The crystal basis theory and it's related combinatorics, initiated by Kashiwara in the beginning of 1990, provide alternative way to compute such weight multiplicities. For example, by enumerating Kashiwara-Nakashima tableaux with a fixed weight, one can compute weight multiplicities. But the description of Kashiwara-Nakashima tableaux is somewhat complicated. Thus it looks difficult to compute multiplicities by using Kashiwara-Nakashima tableaux in general.

In the joint work of Kyu-Hwan Lee and Jangsoo Kim, we suggest new families of tableaux, called (spin-)rigid tableaux, which are subsets of standard (skew) Young tableaux and are equinumerous to weight multiplicities of certain infinite families of highest modules over finite finite simple Lie algebra types B and D. Moreover, we can give explicit and closed formulas for certain subfamilies of them. Interestingly, they form Pascal, Catalan, Motzkin, Riordan(newly defined by ourselves) and Bessel triangular arrays.

Student Combinatorics Seminar

Geometry on the space of Kahler metrics and applications to canonical metrics

##### Abstract:

A basic problem in Kahler geometry, going back to Calabi in the 50's, is to find Kahler metrics with the best curvature properties, e.g., Einstein metrics. Such special metrics are minimizers of well known functionals on the space of all Kahler metrics H. However these functionals become convex only if an adequate geometry is chosen on H. One such choice of Riemannian geometry was proposed by Mabuchi in the 80's, and was used to address a number of uniqueness questions in the theory. In this talk I will present more general Finsler geometries on H, that still enjoy many of the properties that Mabuchi's geometry has, and I will give applications related to existence of special Kahler metrics, including the recent resolution of Tian's related properness conjectures.

Symplectic Deformation of simple Hamiltonian-S^1 Manifolds

##### Abstract:

Recently, an interesting symplectic deformation on simple Hamiltonian-S^1 manifolds of dimension 6 was constructed and described. It had the auspicious property of producing a deformation equivalence between a Kaehler form and a symplectic form that was not Hard Lefschetz, thereby answering a question from Khesin and McDuff in the 1990s. I will present work on extending this result to dimensions 8 and higher.

Welcome Week

Student Number Theory Seminar

Commutative Algebra Seminar

Structure at Infinity for Shrinking Ricci Solitons

PDE Seminar

Algebraic Geometry Seminar

Student Algebraic Topology Seminar

Recent Progress in Representation Stability

##### Abstract:

Representation stability is a relatively new field that studies somewhat exotic algebraic structures and exploits their properties to prove results (often asymptotic in nature) about objects of interest. I will describe some of the algebraic structures that appear (and state some important results about them), give a sampling of some notable applications (in group theory, topology, and algebraic geometry), and mention some open problems in the area.

What is special about mining spatial and spatio-temporal datasets?

##### Abstract:

The importance of spatial and spatio-temporal data mining is growing with the increasing incidence and importance of large datasets such as trajectories, maps, remote-sensing images, census and geo-social media. Applications include Public Health (e.g. monitoring spread of disease, spatial disparity, food deserts), Public Safety (e.g. crime hot spots), Public Security (e.g. common operational picture), Environment and Climate (change detection, land-cover classification), M(obile)-commerce (e.g. location-based services), etc.

Classical data mining techniques often perform poorly when applied to spatial and spatio-temporal data sets because of the many reasons. First, these dataset are embedded in continuous space with implicit relationships, whereas classical datasets (e.g. transactions) are often discrete. Second, the cost of spurious patterns (e.g., false positives, chance patterns) is often high in spatial application domains. In addition, one of the common assumptions in classical statistical analysis is that data samples are independently generated. When it comes to the analysis of spatial and spatio-temporal data, however, the assumption about the independence of samples is generally false because such data tends to be highly self correlated. For example, people with similar characteristics, occupation and background tend to cluster together in the same neighborhoods. In spatial statistics this tendency is called autocorrelation. Ignoring autocorrelation when analyzing data with spatial and spatio-temporal characteristics may produce hypotheses or models that are inaccurate or inconsistent with the data set.

Thus new methods are needed to analyze spatial and spatio-temporal data to discover interesting, useful and non-trivial patterns. This talk surveys some of the new methods including those for discovering hotspots (e.g., circular, linear, rings), interactions (e.g. co-locations , co-occurrences, tele-connections), detecting spatial outliers and location prediction along with emerging ideas on spatio-temporal pattern mining.

Shashi Shekhar is a Mcknight Distinguished University Professor at the University of Minnesota (Computer Science faculty). For contributions to geographic information systems (GIS), spatial databases, and spatial data mining, he was elected an IEEE Fellow as well as an AAAS Fellow and received the IEEE-CS Technical Achievement Award, and the UCGIS Education Award. He was also named a key difference-maker for the field of

Climate Change Seminar

Automorphic Forms & Number Theory [will not meet]

##### Abstract:

Room tba

Integral Structures on DeRham Cohomology

##### Abstract:

Given a smooth projective variety X over a number field K, we construct two canonical O_K-lattices in the algebraic de Rham cohomology of X. The first is constructed using the p-adic comparison theorems (for all p). The second is constructed geometrically, but the proof that it is a lattice uses the p-adic comparison theorems. Both constructions have more elementary analogs in complex geometry that I will discuss first. This is joint work with Bhargav Bhatt.

Cockburn's Seminar

MCFAM Seminar - No Seminar

The effect of clamped intervals on the representations of posets

##### Abstract:

In work with Kos Diveris and Marju Purin we show that subintervals of a poset satisfying a condition that we call 'clamped' determine a part of the representation theory of the whole poset, to the extent that we can determine the Auslander-Reiten quivers of the bounded derived category and of the module category in favorable circumstances. The approach allows us to construct lattices with quivers of arbitrary tree class (up to barycentric subdivision), as well as lattices of finite representation type, derived equivalent to quivers of wild representation type

Exploring Citation Networks

##### Abstract:

Citation graphs are at the core of expert knowledge propagation and verification, regardless of domain, whether legal or scientific. We discuss two projects that explore citation graphs. Specifically, we define the problems, propose our methodology, as well as demonstrate the challenges and results. The first project looks at legal precedent, and the second focuses on the impact of scientific retraction.

Turbulent Weak Solutions of the Euler Equations

##### Abstract:

Motivated by Kolmogorov's theory of hydrodynamic turbulence, we consider dissipative weak solutions to the 3D incompressible Euler equations. We show that there exist infinitely many weak solutions of the 3D Euler equations, which are continuous in time, lie in a Sobolev space $H^s$ with respect to space, and they do not conserve the kinetic energy. Here the smoothness parameter $s$ is at the Onsager critical value $1/3$, consistent with Kolmogorov's $-4/5$ law for the third-order structure functions. We shall also discuss bounds for the second order structure functions, which deviate from the classical Kolmogorov 1941 theory. This talk is based on joint work with T. Buckmaster and N. Masmoudi.

Geodesics on Surfaces

##### Abstract:

Let S be a hyperbolic surface. We will give a history of counting results for geodesics on S. In particular, we will give estimates that fill the gap between the classical results of Margulis and the more recent results of Mirzakhani. We will then give some applications of these results to the geometry of curves. In the process we highlight how combinatorial properties of curves, such as self-intersection number, influence their geometry.

Math Club Welcome Week

Commutative Algebra Seminar - No Seminar

Superlensing Using Hyperbolic Metamaterials

##### Abstract:

We discuss super-lensing in composite media, i.e., the possibility of imaging an arbitrary object without imposing any conditions on size of the object and the wave length. We are particularly interested in lenses made of hyperbolic metamaterials and propose two devices that exhibit superlensing properties. This is joint work with Hoai-Min Nguyen (EPFL).

Geometric Analysis Learning Seminar

PDE Seminar

Climate Change Seminar

Automorphic Forms and Number Theory

MCFAM Seminar

Commutative Algebra Seminar - No Seminar

Climate Change Seminar

Commutative Algebra Seminar

Climate Change Seminar

MCFAM Seminar

Commutative Algebra Seminar

Climate Change Seminar

MCFAM Seminar - No Seminar

Commutative Algebra Seminar

Climate Change Seminar

Plane wave approximation of homogeneous Helmholtz solutions

##### Abstract:

We establish error estimates for the approximation of solutions of the Helmholtz equation by linear combinations of plane waves. The estimates combine approximation results of Helmholtz solutions by generalized harmonic polynomials, via Vekua theory, and approximation of generalized harmonic polynomials by plane waves.

Reading Seminar for Automorphic Forms

MCFAM Seminar

Lie Theory Seminar

Applied and Computational Math Colloquium

Student Combinatorics Seminar

Colloquium

Algebraic Geometry Reading Group Seminar

Differential Geometry and Symplectic Topology seminar

Math Physics Seminar

Commutative Algebra Seminar

Geometric Analysis Learning Seminar

Large time behavior of Trudinger's equation

##### Abstract:

We will study the large time behavior of a homogeneous doubly nonlinear flow. This equation is among a class of

nonlinear parabolic PDE for which Trudinger established a Harnack inequality by generalizing previous work of Moser.

We will show that the large time behavior is tied to equality conditions of an optimal Poincaré inequality and its "dual." Conversely,

we will explain how to write down a flow that will help approximate the optimal constant for any Poincaré type inequality and its extremal

functions. Time permitting, we will discuss applications to nonlocal equations and to the operator norm of the Sobolev trace mapping.

Algebraic Geometry Seminar

Algebraic Geometry Seminar

Self-Adjoint Operators on a Modular Curve: why a number theorist is allowed to talk in a PDE Seminar

##### Abstract:

It was speculated by Hilbert and Polya that one might solve the Riemann Hypothesis by finding self-adjoint operator whose spectral parameters contained zeros of zeta. However, little progress has been made in this direction due to a lack candidate operators. In 1977 a computational mistake inspired some recent traction by Bombieri and Garrett.

Differential Geometry and Symplectic Topology seminar

Climate Change Seminar

[will not meet]

Approximating Functions with Singularities

##### Abstract:

Title: Approximating Functions with Singularities

Topology Seminar

Student Number Theory Seminar

Reading Seminar for Automorphic Forms

A reduced-form model for level-1 limit order books

##### Abstract:

One popular approach to model the limit order books dynamics of the

best bid and ask at level-1 is to use the reduced-form diffusion

approximations. It is well known that the biggest contributing factor

to the price movement is the imbalance of the best bid and ask. We

investigate the data of the level-1 limit order books of a basket of

stocks and study the numerical evidence of drift, correlation,

volatility and their dependence on the imbalance. Based on the

numerical discoveries, we develop a nonparametric discrete model for

the dynamics of the best bid and ask, which can be approximated by a

reduced-form model with analytical tractability that can fit the

empirical data of correlation, volatilities and probability of price

movement simultaneously.

This is a joint work with Prof. Lingjiong Zhu.

Bio: Dr. Tzu-Wei Yang was a post-doctoral fellow at Stanford University's Department of Mathematics prior to joining MCFAM. He got his PhD from the Institute for Computational and Mathematical Engineering at Stanford University where his advisor was Dr. George C. Papanicolaou, the Robert Grimmett Professor of Mathematics at Stanford. Dr. Yang's research interests cover stochastic differential equations, financial mathematics and uncertainty quantification. Dr. Yang also has a B.S in Applied Mathematics from National Chiao Tung University, and an MS in Electrical Engineering from National Taiwan University in Taiwan.

More details on his current research can be found at:http://math.umn.edu/~yangx953/

A rational lift of the combinatorial R-matrix

##### Abstract:

The combinatorial R-matrix is the unique affine $\mathfrak{sl}_n$ crystal isomorphism between $B_1 \otimes B_2$ and $B_2 \otimes B_1$, where $B_1$ and $B_2$ are finite-dimensional affine crystals corresponding to rectangular partitions. This map can be described combinatorially in terms of rectification of skew tableaux.

In this talk, I will present a construction of a ``geometric R-matrix,'' a rational map which has properties analogous to those of the combinatorial R-matrix, and which tropicalizes to give a piecewise-linear formula for the combinatorial R-matrix. The construction makes use of Noumi and Yamada's notion of ``tropical row insertion,'' as well as the Grassmannian and the loop group. When both partitions are a single row, we recover results of Yamada and Lam-Pylyavskyy.

Lie Theory Seminar

Applied and Computational Math Colloquium

Recent Advances in Symmetrization Techniques for Nonlocal Equations

##### Abstract:

Symmetrization techniques are nowadays widely renowned for being very efficient tools to get sharp estimates for solutions to PDE. In the first part of this talk, excerpted from the joint work with G. Di Blasio, we shall describe how symmetrization techniques allow to get a concentration comparison result for solutions of elliptic equations involving the fractional Laplacian, of the type $(-\Delta)^{\alpha/2}u=f$ posed in an open bounded set $\Omega$ of R^N and 0 < \alpha < 2, with homogeneous Dirichlet boundary conditions. The data f is assumed to belong to a suitable Lorentz space $L^{p,q}(\Omega)$. These results will be useful to easily obtain, as a natural consequence, some regularity results for the solutions in terms of the data f, generalizing the classical results for the Laplacian. The second part of the talk will focus on the main topics of some recent joint works with J. L. Vázquez in which we consider the application of symmetrization techniques to obtaining concentration comparison results for linear and nonlinear parabolic equations with fractional diffusion, of the form $u_{t}+(-\Delta)^{\alpha/2}A(u)=f$, taking into account several assumptions on the nonlinearity $A:\R_{+}\rightarrow\R_{+}$. Moreover, we will show some very recent results where Neumann boundary conditions are assumed. Finally, we will sketch some work in progress in the theory, concerning the application of these methods to nonlocal operators related to the the gaussian measure.

Soumitri Kolavennu: Critical Node Analysis and Mitigation in Industrial Wireless Sensor Networks (Applications of Spectral Graph theory)

##### Abstract:

Honeywell’s automation and control solutions unit consists of a number businesses where wireless sensor networks are utilized. These wireless networks provide total install cost savings for the business and its customers. In addition, during operation the systems are more robust to link and node failures. Wireless sensor networks are employed in industrial control and data acquisition systems, hotel management networks, automated meter reading networks, building scale fire and life safety systems etc.

The wireless sensor networks are deployed as mesh networks where the sensor and actuator nodes can talk to each other neighbors and reach destination nodes which are typically gateways where the data is consumed. Mesh networks are desirable because of the inherent ability of the network to reconfigure itself around a faulted node or a link and still be able to reach the gateway. However such guarantees are only possible when there are no critical nodes (nodes that split the network into disjoint clusters). This talk concentrates on ability of the network management functions to detect critical nodes quickly and provide mitigation for the critical nodes and links using spectral graph theory. Other applications of spectral graph theory for these networks are also discussed. The main motivation of the presentation is to present the typical kinds of problems in practical implementation of sensor networks in the automation and control industries.

Soumitri Kolavennu joined Honeywell in 1999, initially as a student intern. His areas of expertise include wireless, voice, and advanced control. His early work in wireless mesh networking and wireless localization enabled ACS products like OneWireless™ and Impact Xtreme to be differentiated in the marketplace. Recently, He has been a key contributor to Honeywell’s Connected Home offerings, specifically the Voice recognition and Home Kit based thermostats. He was the primary contributor and editor for the Networking and Provisioning Layers of the ISA100.11a standard for industrial wireless sensor networks and he has helped draft standards relevant to the smart grid and energy management systems. He is a member of the Standards Subcommittee of IEEE Control Systems Society and a past member of the Smart Grid Architecture Committee (SGAC) for the NIST Smart Grid Interoperability Panel (SGIP). He is the fellows leader for Homes and Building technologies with in Honeywell. He has over 50 issued patents. His publications

Marc Light: Lecture

Student Combinatorics Seminar

Colloquium

BMO solvability and absolute continuity of harmonic measure

##### Abstract:

For a uniformly elliptic divergence form operator $L$, defined in an open set

$\Omega$ with Ahlfors-David regular boundary, we show that BMO-solvability implies scale invariant quantitative absolute continuity (the weak-$A_\infty$ property) of elliptic-harmonic measure with respect to surface measure on $\partial \Omega$. We do not impose any connectivity hypothesis, qualitative or quantitative; in particular, we do not assume the Harnack Chain condition, even within individual connected components of $\Omega$.

In this generality, our results are new even for the Laplacian. Moreover, we obtain a converse, under the additional assumption that $\Omega$ satisfies an interior Corkscrew condition, in the special case that $L$ is the Laplacian. This is joint work with Phi Le.

Algebraic Geometry Reading Group Seminar

Differential Geometry and Symplectic Topology seminar

SIAM Student Chapter Reading Group Seminar

##### Abstract:

12/8/16 Seminar Location Change to 140 Nolte Center for Continuing Education

Green's Functions In Curved Spacetimes And Gravitational Waves

##### Abstract:

Green's functions lie at the heart of constructing (perturbative) solutions to both linear and nonlinear wave equations of mathematical physics. In curved spacetimes, they are also key to understanding the causal structure of their radiative wave solutions: for, despite having a zero rest mass, photons and gravitons travel both on and within the null cone in a generic curved geometry. (This inside-the-null cone propagation of waves is called the "tail effect" and is also sometimes described as a violation of Huygens' principle.) I will explain, in particular, why Green's functions in black hole (BH) geometries play a crucial role in understanding the gravitational waves (GWs) emitted from the super-massive BHs that astronomers now believe reside at the center of most (if not all) galaxies, including our own. Within the next 2 decades, humanity may have the means -- by orbiting very large scale GW detectors around the Sun -- to directly hear such vibrations of spacetime. I am developing a research program to explore novel methods to compute curved spacetime Green's functions, and will review some of my results.

Math Club

Uniform Asymptotic Growth on Symbolic Powers of Ideals

##### Abstract:

More recently, my dissertation (e.g., arxiv.org/1510.02993, arxiv.org/1608.02320) attempts to devise--and establish affirmative results towards--a "toric" variant of a short-lived conjecture of Brian Harbourne (2009) that says: For N \ge 2, the symbolic power I^{(N(r-1)+1)} lies in I^r for all r>0 and all graded ideals I in the coordinate ring R of a projective N-space over a field (sometimes arbitrary, sometimes not). This talk will discuss criteria for ideal containments of type I^{(E(r-1)+1)} \subseteq I^r for all r>0: at the expense of focusing rigidly on a very specific type of ideal, I can give you a duly explicit slope E. These criteria already apply to a fairly prodigious class of normal domains (e.g., several with European-honorific names).

Geometric Analysis Learning Seminar

SIAM Student Chapter Reading Group Seminar

Phase separation patterns from directional quenching

##### Abstract:

We study the effect of directional quenching on patterns formed in simple bistable systems such as the Allen-Cahn and the Cahn-Hilliard equation on the plane. We model directional quenching as an externally triggered change in system parameters, changing the system from monostable to bistable across an interface. We are then interested in patterns forming in the bistable region, in particular as the trigger progresses and increases the bistable region. We find existence and non-existence results of single interfaces and striped patterns. Joint work with Arnd Scheel.

Lifting laws, arithmetic invariant theory, and L-functions

##### Abstract:

I will discuss, by way of examples, how arithmetic invariant theory seems to play a non-trivial role in the theory of integral representations of L-functions. The examples include results of many people, such as Andrianov, Avner Segal, and myself. With these examples as motivation, I will then discuss my recent work on twisted versions of some of the orbit parametrization theorems of Bhargava. The main technical ingredient in the proof of these parametrizations is a "lifting law", which is a way of relating elements in the open orbit of one prehomogeneous vector space with elements in the minimal orbit of another prehomogeneous vector space.

A New Discriminant Algebra Construction

##### Abstract:

For a finite separable field extension in characteristic other than 2, its discriminant field controls whether its Galois closure has Galois group contained in the alternating group. In the last decade, Rost, Deligne, and Loos have suggested generalizations of the discriminant field to a "discriminant algebra" defined for general branched covers of schemes. We present a new construction of a discriminant algebra and discuss its relation to those defined by Rost and Loos. This is joint work with Alberto Gioia.

A New Discriminant Algebra Construction

##### Abstract:

For a finite separable field extension in characteristic other than 2, its discriminant field controls whether its Galois closure has Galois group contained in the alternating group. In the last decade, Rost, Deligne, and Loos have suggested generalizations of the discriminant field to a "discriminant algebra" defined for general branched covers of schemes. We present a new construction of a discriminant algebra and discuss its relation to those defined by Rost and Loos. This is joint work with Alberto Gioia.

Frechet Differentiability in the Optimal Control of the Stefan Problem

##### Abstract:

In this talk I will give a heuristic derivation for the Frechet gradient in the optimal control of a Stefan-type free boundary problem. I will introduce the notion of the adjoint problem, which is analogous to the method of Lagrange multipliers. I will show how the heuristic derivation can be used to prove the derivative formula rigorously. This work was completed as part of an REU at the Florida Institute of Technology led by Professor Ugur Abdulla.

Arithmetic Invariant Theory

##### Abstract:

Arithmetic invariant theory is, roughly, the study of the orbits of groups like GL_n(Z) on lattices inside the finite dimensional representations of GL_n(R). While simply stated, these orbit problems turn out to be delicate and interesting. I will give an introduction to and partial survey of this field. In particular, I will highlight "Gauss composition" on binary quadratic forms, and some of the seminal contributions of Bhargava on "Higher composition laws".

Differential Geometry and Symplectic Topology seminar

Climate Change Seminar

Variable coefficients and numerical methods for electrmagnetic waves

##### Abstract:

In the first part of the talk, we will discuss a numerical method for

wave propagation in inhomogeneous media. The Trefftz method relies on

basis functions that are solution of the homogeneous equation. In the

case of variable coefficients, basis functions are designed to solve an

approximation of the homogeneous equation. The design process yields

high order interpolation properties for solutions of the homogeneous

equation. This introduces a consistency error, requiring a specific

analysis.

In the second part of the talk, we will discuss a numerical method for

elliptic partial differential equations on manifolds. In this framework

the geometry of the manifold introduces variable coefficients. Fast,

high order, pseudo-spectral algorithms were developed for inverting the

Laplace-Beltrami operator and computing the Hodge decomposition of a

tangential vector field on closed surfaces of genus one in a three

dimensional space. Robust, well-conditioned solvers for the Maxwell

equations will rely on these algorithms.

[will not meet]

Approximating Functions with Singularities

##### Abstract:

Title: Approximating Functions with Singularities

Student Number Theory Seminar

Quantization of the Modular Functor and Equivariant Elliptic Cohomology

##### Abstract:

Let M be a compact G-space for a compact Lie group G. I will describe a procedure that can be seen as the categorical quantization of the category of parametrized positive energy representations of the loop group of G. This procedure is described in terms of dominant K-theory of the loop group parametrized over M. More concretely, I will construct a holomorphic sheaf over a universal elliptic curve with values in dominant K-theory of the loop space LM, and show that each stalk of this sheaf is a cohomological functor of M (thereby giving rise to an equivariant cohomology theory). I will also give compelling evidence that this theory is equivalent to equivariant elliptic cohomology of M as constructed by Grojnowski. I will assume very little background, and give a lot of motivation, but some general ideas of what a field theory is may be helpful.

REMINDER: This talk is at 12:20!

Alexander Cloninger: Incorporation of Geometry into Learning Algorithms and Medicine

##### Abstract:

This talk focuses on two instances in which scientific fields outside mathematics benefit from incorporating the geometry of the data. In each instance, the applications area motivates the need for new mathematical approaches and algorithms, and leads to interesting new questions. (1) A method to determine and predict drug treatment effectiveness for patients based off their baseline information. This motivates building a function adapted diffusion operator high dimensional data X when the function F can only be evaluated on large subsets of X, and defining a localized filtration of F and estimation values of F at a finer scale than it is reliable naively. (2) The current empirical success of deep learning in imaging and medical applications, in which theory and understanding is lagging far behind. By assuming the data lies near low dimensional manifolds and building local wavelet frames, we improve on existing theory that breaks down when the ambient dimension is large (the regime in which deep learning has seen the most success).

Reading Seminar for Automorphic Forms

Industry Competition, Profitability and Stock Returns

##### Abstract:

Speaker: Yao Deng

Affiliation: UMN Carlson PhD in Finance Candidate/MCFAM MFM Alumnus

Bio: Yao Deng is currently a third year finance PhD student at University of Minnesota. His research interests include empirical and theoretical asset pricing, macro finance and behavioral finance. He holds a master in financial mathematics from University of Minnesota and a bachelor in economics and mathematics from Central University of Finance and Economics in Beijing.

The orbit method via deformations of singular symplectic varieties

##### Abstract:

One of the cornerstones of the infinite dimensional Lie representation theory is Kirillov's Orbit method (1961). It says that the irreducible unitary representations of a nilpotent Lie group are in a natural bijection with the orbits of the coadjoint action of that group. There is an analog of this result for nilpotent Lie algebras, due to Dixmier (1963): instead of unitary representations one considers so called primitive ideals ( = annihilators of irreducible modules) in universal enveloping algebras.

An immediate question is how to generalize these results to semisimple Lie groups or Lie algebras. I will talk about the Lie algebra case. My recent result here is that there is a natural map from the set of (co)adjoint orbits to the set of primitive ideals which is known to be injective in almost all cases (for example, for classical Lie algebras). To produce this map I compare commutative and noncommutative deformations of singular symplectic varieties, a spectacular class of singular algebraic varieties introduced by Beauville in 2000.

Stefan Steinerberger: Elliptic PDEs and Diffusion: Short Proofs by Counting Particles and Applications

##### Abstract:

We describe a simple trick in the study of elliptic PDEs: introduce time and interpret the solution of the elliptic pde as a fixed point of the evolution of the parabolic equation. We illustrate this technique by giving extremely short proofs of some classical results, an alternative interpretation of the Filoche-Mayboroda landscape function and improvements of classical results of Makai, Hayman and E. Lieb (originally conjectured by Polya & Szego). Finally, we discuss applications in data science (related to properties of eigenfunctions of Graph Laplacians on graphs constructed from real-life data).

Applied and Computational Math Colloquium

Exotic cluster algebras

##### Abstract:

Cluster algebras are commutative rings with a distinguished set of generators that are grouped into overlapping finite sets of the same cardinality. Among many other examples, cluster algebras appear in coordinate rings of various algebraic varieties. Using the notion of compatibility between Poisson brackets and cluster algebras in the coordinate rings of simple complex Lie groups, Gekhtman Shapiro and Vainshtein conjectured a correspondence between the two. Poisson Lie groups are classified by the Belavin-Drinfeld classification of solutions to the classical Yang Baxter equation. For a simple complex Lie group G and a Belavin-Drinfeld class, one can define a corresponding Poisson bracket on the ring of regular

functions on G. For some of these classes a compatible cluster structure can be constructed.

Probability Semianr - No Seminar

Jesse Berwald, Ryan Siskind: High-dimensional Retail

##### Abstract:

For many problems encountered in industry a mathematical solution lands the user in a high dimensional space. Often the space is sparse even given terabytes of data. We discuss some approaches to these problems in the context of recently implemented products at Target.

Student Combinatorics Seminar

Asymptotic representation theory over Z

##### Abstract:

Representation theory over Z is famously intractable, but "representation stability" provides a way to get around these difficulties, at least asymptotically, by enlarging our groups until they behave more like commutative rings. Moreover, it turns out that important questions in topology/number theory/representation theory/... correspond to asking whether familiar algebraic properties hold for these "rings". I'll explain how these connections work; describe what we know and don't know; and give a wide sampling of applications in different fields where this has led to concrete results. No knowledge of representation theory will be required -- indeed, that's sort of the whole point!

Large Time Behaviour in Fisher-KPP Type Equations

##### Abstract:

The Fisher-KPP (Kolmogorov, Petrovskii, Piskunov) equation in one space variable is one of the simplest looking reaction-diffusion equations. The solution starting from a Heaviside initial datum will converge, up to a nontrivial logarithmic time delay, to a travelling wave. This result was proved by Bramson in the early 80's, using elaborate probabilistic arguments. We will present a simple PDE proof of this result, and discuss some extensions, such as sharp asymptotics, time inhomogeneous equations, problems in several space dimensions.

Joint work with J. Nolen and L. Ryzhik.

Algebraic Geometry Reading Group Seminar

New Interactions between Analysis and Number Theory

##### Abstract:

I will discuss three different topics that connect classical analysis

with number theory in a new and unexpected way (remarks and comments

are very much appreciated!). (1) A new type of Poincare inequality on

the Torus that is optimal in all sort of ways, scales, exponents,...

and possibly suggests new families of inequalities somewhere between

elliptic estimates and dynamical systems. (2a) If the classical

Hardy-Littlewood maximal function of a function f(x) is easy to

compute, the function is f(x) = sin(x) or, equivalently, (2b) if f(x)

is periodic and the trapezoidal rule is sharp on all intervals of

length 1, then the function is trigonometric. This statement is

clearly very elementary but the only proof I could find has to use

transcendental number theory and I am not sure why! (3) Finally,

just for fun, strange, unexplained (and pretty!) patterns that appear

in an old integer sequence of Stanislaw Ulam [Prize Money: $200

dollars for an explanation/proof] and an amusing trigonometric-type

function with fractal properties.

SIAM Student Chapter Reading Group Seminar

Differential Geometry and Symplectic Topology seminar - No Seminar

Math Club

Math Physics Seminar

##### Abstract:

It is well known that both classical and quantum mechanical systems are described as Hamiltonian systems: finite-dimensional one for the former, and infinite-dimensional for the latter with respect to appropriate symplectic structures. I will show how to exploit such geometric structures to formulate semiclassical dynamics---the transition regime between quantum and classical mechanics---from the symplectic-geometric point of view. Of particular interest is the semiclassical wave packets of Hagedorn. I will explain how one can formulate the dynamics of the wave packets from the symplectic/Hamiltonian point of view.

Commutative Algebra Seminar

Ricci flow on manifolds with positive isotropic curvature

Aaron Welters: Toward a Theory of Broadband Absorption Suppression in Magnetic Composites

##### Abstract:

A major problem with magnetic materials in application is they naturally have high losses in a wide frequency range of interest (e.g., Faraday rotation using ferromagnets in optical frequencies). Composites can inherit significantly altered properties from those of their components. Does this apply to losses and magnetic properties? How can broadband absorption suppression in magnetic-dielectric composites be achieved? In this talk, I will discuss our developments toward a theory of broadband absorption suppression in magnetic composites based on a Lagrangian and Hamiltonian approach from classical mechanics. In the first part of the talk, I will introduce the hierarchy of models we are using, based on two-component composite linear systems with a high-loss and a lossless component, for studying the interplay of dissipation (losses) and gyroscopy (magnetism) as well as the dominant mechanisms of energy loss. Next, I will discuss our new results towards answering these questions related to the modal dichotomy and selective overdamping phenomena in systems with finite degrees-of-freedom (e.g., electric circuits with gyrators and resistors). I will conclude the talk with our recent developments of this theory for Maxwell's equations pertaining to the dissipative properties of electromagnetic fields in stratified magnetic-dielectric media. This is joint work with Alex Figotin (UCI) and Robert Viator (IMA).

SIAM Student Chapter Reading Group Seminar

The singular free boundary in the Signorini problem

##### Abstract:

In this talk I will overview the Signorini problem for a divergence form elliptic operator with Lipschitz coefficients, and I will describe a few methods used to tackle two fundamental questions: what is the optimal regularity of the solution, and what can be said about the singular free boundary in the case of zero thin obstacle. The proofs are based on Weiss and Monneau type monotonicity formulas.

This is joint work with Nicola Garofalo and Arshak Petrosyan

Algebraic Geometry Seminar

Fundamental Solutions for 2nd Order Elliptic Operators

##### Abstract:

Fundamental solutions are central objects in the study of linear differential equations. I will review some ways that they are useful and some of their key properties in the context of 2nd order elliptic PDE. Then I will present recent results on existence and estimates of the fundamental solution for 2nd order equations with lower order terms. This latter part will be based on joint work with Svitlana Mayboroda and Blair Davey (City College of New York).

Joakim Anden: Three-Dimensional Covariance Estimation from Noisy Tomographic Projections

##### Abstract:

Particles imaged in cryo-electron microscopy (cryo-EM) often do not exist in a single molecular structure but exhibit significant structural variability. To determine the biological function of a particle, it is important to characterize this variability given noisy projection images, a task known as the heterogeneity problem in single-particle cryo-EM. We present an efficient and accurate method for estimating the low-rank covariance matrix of the three-dimensional voxel structure, which in turn allows for reconstruction of the molecular structure corresponding to each image. The method poses the covariance estimation task as a linear inverse problem in the covariance matrix elements and calculates its least-squares estimator. An efficient algorithm is obtained by exploiting the convolutional structure of the normal equations and reformulating them as a deconvolution problem which can be solved using the conjugate gradient method. The resulting method is the first computationally tractable algorithm for three-dimensional covariance estimation in cryo-EM that is also consistent. Its performance is evaluated on various datasets, demonstrating its effectiveness in solving the heterogeneity problem for both simulations and experimental data.

Differential Geometry and Symplectic Topology seminar

Climate Change Seminar

Automorphic Forms and Number Theory [will not meet]

Approximating Functions with Singularities

##### Abstract:

Title: Approximating Functions with Singularities

Topology Seminar

Singular Stochastic PDEs - How do they arise and what do they mean?

##### Abstract:

Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.

Student Number Theory Seminar

Reading Seminar for Automorphic Forms

MCFAM Seminar - No Seminar

MCFAM Seminar- Thanksgiving

Combinatorics Seminar

Lie Theory Seminar

No seminar

Applied and Computational Math Colloquium

Student Combinatorics Seminar

Colloquium

Algebraic Geometry Reading Group Seminar

SIAM Student Chapter Reading Group Seminar

Differential Geometry and Symplectic Topology seminar

Math Physics Seminar

Math Club

Commutative Algebra Seminar

Geometric Analysis Learning Seminar

SIAM Student Chapter Reading Group Seminar

PDE Seminar

Algebraic Geometry Seminar

Differential Geometry and Symplectic Topology seminar

Climate Change Seminar

Approximating Functions with Singularities

##### Abstract:

Title: Approximating Functions with Singularities

[will not meet]

Alexander Cloninger: Lecture

Topology Seminar

##### Abstract:

TBA

TASEP on a ring in relaxation time scale

##### Abstract:

Consider the totally asymmetric simple exclusion process (TASEP) on a ring of size $L$. It has been conjectured since 80's that the system starts to relax when time $t$ is of order $L^{3/2}$. In the sub-relaxation time scale, the system size has little effect on the particle fluctuations and hence the system belongs to the so-called KPZ universality class, in which the fluctuations are of order $t^{1/3}$ and the limiting distributions depend only on the initial data. And after relaxation time scale, the system reaches its equilibrium and the limiting distribution is given by Gaussian distribution which is independent of the initial data.

In this talk, we will show the crossover limiting distributions in relaxation time scale for three classical initial conditions. These crossover distributions interpolate the distributions in KPZ universality class and the Gaussian distribution, and should be universal for any periodic system in KPZ universality class with similar initial data.

Student Number Theory Seminar

Reading Seminar for Automorphic Forms

MCFAM Seminar - No Seminar

Hiding a Secret in Plain Sight!

##### Abstract:

A rotation map labeling result for regular graphs is derived and then applied in a privacy preserving protocol. It allows a group to give a key to a member, in such a way that no one in the group knows who has the key, except the key holder.

Lie Theory Seminar

Applied and Computational Math Colloquium

Density maximums and a generalization of Rogozin

##### Abstract:

We will present some rather general extensions of an inequality due to Rogozin concerning the essential supremum of a convolution of \(k\)probability density functions on the real line. Though weakened versions of the theorem will be stated in the context of arbitrary unimodular locally compact groups when \(k = 2\), we will focus on applications to \(\mathbb{R}^d\) where the result can combined with rearrangement inequalities for arbitrary k to recover a full generalization. As a consequence, we obtain a unification and sharpening of both the \(\infty\)-Renyi entropy power inequality for sums of independent random vectors, due to Bobkov and Chistyakov and the bounds on marginals of projections of product measures due to Rudelson-Vershynin (which match the sharp improvement Livshyts-Paouris-Pivovarov). The proof is elementary and relies on a characterization of extreme points of a class of probability measures in the general setting of Polish measure spaces, and the development of a generalization of Ball's cube slicing bounds for products of \(d\) dimensional balls where the ``co-dimension 1-type" case had been recently settled by Brzezinski.

Arnaub Chatterjee: Practical Applications of Health Data

##### Abstract:

This talk aims to delineate how different players of the healthcare ecosystem are taking advantage of data liquidity and how data is being utilized to align the practice of medicine to evidence-based care. We will discuss the evolution of big data (including claims, clinical, genomic and social media data, among others) in the healthcare ecosystem and different types of structured and unstructured data will be reviewed. The use of technology and analytics to structure and present information will be examined. The talk will focus heavily on real world case studies to draw insights from payer, provider, government, pharmaceutical and the startup domains to see how organizations are using real world data to create pathways to value. Arnaub Chatterjee is Director of the Data Science and Insights group at Merck. Additionally, he serves as Lecturer in the Department of Policy Analysis and Management at Cornell University and is Teaching Associate in the Department of Health Care Policy at Harvard Medical School. At Merck, he is responsible for leading ventures and partnerships with academic medical centers, payers and technology companies around the novel use of health data and analytics in improving patient care. Previously, he worked for the Obama Administration serving as an advisor to former Chief Technology Officers Todd Park and Bryan Sivak at the U.S. Department of Health and Human Services (HHS). At HHS, he co-led efforts for the Health Data Initiative, designed the www.healthdata.gov platform, and launched the Innovation Fellows Program. He previously worked in the Secretary's Office as a lead policy analyst on healthcare fraud and abuse policy initiatives around the Affordable Care Act. Prior to government service, he spent a number of years as a strategy consultant at Deloitte Consulting, advising hospitals, payers and state governments on how to navigate financial and policy challenges. Arnaub's work has appeared in a variety of publications, including the Journal of the American College of Cardiology and the American Journal for Managed Care and he has presented at a number of conferences ranging from South by Southwest to the Society of General Internal Medicine. He sits on the boards of the Sloan Program at Cornell University and the Stanford Medicine X Precision Medicine initiative. He holds graduate degrees in health administration (MHA) and public administration (MPA) from Cornell University and received his undergraduate degree from

Student Combinatorics Seminar

Colloquium

Algebraic Geometry Reading Group Seminar

SIAM Student Chapter Reading Group Seminar

Differential Geometry and Symplectic Topology seminar

2D 2nd order Laplace superintegrable systems, Heun equations, QES and B\^ocher contractions

##### Abstract:

Second-order conformal quantum superintegrable systems in 2 dimensions are Laplace equations with scalar potential and 3 independent 2nd order conformal symmetry operators. They encode all the information about 2D Helmholtz superintegrable systems in an efficient manner: Each of these systems admits a quadratic symmetry algebra (not usually a Lie algebra) and is multiseparable. The separation equations comprise all of the various types of hypergeometric and Heun equations in full generality. In particular, they yield all of the 1D Schr\"odinger exactly solvable (ES) and quasi-exactly solvable (QES) systems related to the Heun operator. The separable solutions of these equations are the special functions of mathematical physics. The different systems are related by St\"ackel transforms, by the symmetry algebras and by B\^ocher contractions of the conformal algebra so(4,C) to itself, which enables all systems to be derived from a single one: the generic potential on the complex 2-sphere. Distinct separable bases for a single Laplace system are related by interbasis expansion coefficients which are themselves special functions, such as the Wilson polynomials. This approach facilitates a unified view of special function theory, incorporating hypergeometric and Heun functions in full generality.

Math Club

The Golod property of Stanley--Reisner rings

##### Abstract:

A graded (or local) ring is called Golod if the Betti numbers of the residue field grow as fast as possible. This is equivalent to the vanishing of all Massey products on the Koszul homology. In this talk, I discuss the latter condition for Stanley--Reisner rings, where one has a geometric interpretation of the product on Koszul homology. I will present several examples to show how one can use geometry to effectively compute these products. In particular, I will present an example where the Golod property depends on the underlying field, and an example where the Koszul homology has a trivial product but a nontrivial ternary Massey product.

Noncompact Shrinking 4 Soliton with Nonnegative Curvature (III)

Peter Monk: Stekloff Eigenvalues in Inverse Scattering

##### Abstract:

We consider a proposed method for non-destructive testing in which small changes in the (possibly complex valued) refractive index of an inhomogeneous medium of compact support are to be determined from changes in measured far field data due to incident plane waves. Discussing first the Helmholtz equation, the problem is studied by considering a modified far field operator whose kernel is the difference of the measured far field pattern due to the scattering object and the far field pattern of an auxiliary scattering problem with the Stekloff boundary condition imposed on the boundary of a domain containing the scattering object. It is shown that scattering data can be used to determine the Stekloff eigenvalues corresponding to this domain. Extensions to Maxwell’s equations will also be presented.

SIAM Student Chapter Reading Group Seminar

The nonlinear Schroedinger equation and the evolution of wave packets in nonlinear dispersive equations

##### Abstract:

The nonlinear Schroedinger equation (NLS) can be derived as a formal approximating equation for the evolution of wave packets in a wide array of nonlinear dispersive PDE’s including the propagation of waves on the surface of an inviscid fluid. In this talk I will describe recent work that justifies this approximation by exploiting analogies with the theory of normal forms for ordinary differential equations.

Algebraic Geometry Seminar

The Characterization of Sobolev Functions as Absolutely Continuous on a.e. Line, and Applications

##### Abstract:

By Morrey's Inequality, it is known that functions in the Sobolev space W^{1,1}(0,1), for example, are exactly the absolutely continuous functions on (0,1). It is also known that such a simple characterization fails in higher dimensions. Nevertheless, an immediate question motivated by Fubini's Theorem is: how does the property of belonging to a Sobolev space compare to the property of having absolute continuity on restrictions to lines? In 1933, Otto Nikodym established the fact that functions in W^{1,p}(R^n) locally are absolutely continuous on almost every line segment and their derivatives satisfy a local L^p-integrability condition. Moreover, a converse of this statement holds. In this talk, a short proof of this result will be shown, followed by two home-cooked applications of this theorem. Namely, we will establish the Chain Rule on the Fundamental Theorem of Calculus when the upper limit is a Sobolev function; and a strong convergence result concerning Steklov averages will be shown

Ornella Mattei: The Theory of Field Patterns

##### Abstract:

Field patterns arise in wave equations with a space-time microstructure. They occur when the microstructure has the interesting feature that a disturbance propagating along a characteristic line, and subsequently interacting with the microstructure, does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is the field pattern. Here we focus on the appearance of field patterns in one spatial dimension plus time. In such a case, the field patterns occur when the slopes of the characteristics and the space-time microstructure are in a sense commensurate.

Teng Zhang: Orthogonal Matrix Retrieval in Cryo-electron Microscopy

##### Abstract:

In single particle reconstruction (SPR) from cryo-electron microscopy (EM), the 3D structure of a molecule needs to be determined from its 2D projection images taken at unknown viewing directions. Zvi Kam showed already in 1980 that the autocorrelation function of the 3D molecule over the rotation group SO(3) can be estimated from 2D projection images whose viewing directions are uniformly distributed over the sphere. The autocorrelation function determines the expansion coefficients of the 3D molecule in spherical harmonics up to an orthogonal matrix. We will show how techniques for solving the phase retrieval problem in X-ray crystallography can be modified for the cryo-EM setup for retrieving the missing orthogonal matrices. Specifically, we present two new approaches that we term Orthogonal Extension and Orthogonal Replacement, in which the main algorithmic components are the singular value decomposition and semidefinite programming. We demonstrate the utility of these approaches through numerical experiments on simulated data. This talk is based joint works with Tejal Bhamre and Amit Singer, available athttps://arxiv.org/abs/1412.0494, https://arxiv.org/abs/1506.02217, and http://arxiv.org/abs/1602.06632.

Differential Geometry and Symplectic Topology seminar

Climate Change Seminar

Automorphic Forms & Number Theory [will not meet]

Approximating Functions with Singularities

##### Abstract:

Title: Approximating Functions with Singularities

The K(2)-local Picard group at p=2

##### Abstract:

The K(n)-local categories provide examples of interesting Picard groups. Their importance in chromatic homotopy theory is highlighted by the fact that the dualizing object for Brown-Commenetz duality comes from an invertible element. These groups have been computed at all primes when n=1 and all odd primes when n=2. Mahowald predicted that the torsion in the K(2)-local Picard group at the prime 2 would be very large compared to the torsion in the K(2)-local Picard groups at odd primes. In this talk, I will confirm this and explain our current understanding of the structure of this group.

Student Number Theory Seminar

Reading Seminar for Automorphic Forms

Evaluations of Hecke algebra traces at Kazhdan-Lusztig basis elements

##### Abstract:

The (type A) Hecke algebra $H_n(q)$ is a certain module over $\mathbb Z[q^{1/2},q^{-1/2}]$ which is a deformation of the group algebra of the symmetric group. The $\mathbb Z[q^{1/2},q^{-1/2}]$-module of its trace functions has rank equal to the number of integer partitions of $n$, and has bases which are natural deformations of those of the symmetric group algebra trace module. While no known formulas give the evaluation of these traces at the natural basis elements of $H_n(q)$, there are some nice combinatorial formulas for the evaulation of certain traces at certain Kazhdan-Lusztig basis elements. We will discuss evaluations of power sum traces, and the open problem of evaluating monomial traces.

Lie Theory Seminar

Applied and Computational Math Colloquium

Optimization on Sparse Random Graphs and its Applications

##### Abstract:

Many optimization problems on sparse random (hyper)graphs are currently intractable to analysis by purely combinatorial techniques. Statistical Physicists predict that the analysis often “simplifies” considerably in the “large degree” limit. In this talk, we will see how to make this idea rigorous by analyzing certain graph cut problems and random constraint satisfaction problems. Our techniques lead to connections between combinatorial problems on sparse random graphs and the study of spin glasses and random matrices.

Parts of this talk will be based on joint work with Amir Dembo and Andrea Montanari.

Cloaking: where Science Fiction meets Science

##### Abstract:

Cloaking involves making an object partly or completely invisible to incoming waves such as sound waves, sea waves or seismic waves, but usually electromagnetic waves such as visible light, microwaves, infrared light, or radio waves. Camouflage and stealth technology achieve partial invisibility, but can one achieve true invisibility from such waves? This lecture will survey some of the wide variety of ideas on cloaking: these include transformation based cloaking, non Euclidean cloaking, cloaking due to anomalous resonance, cloaking by complementary media, active interior cloaking and active exterior cloaking.

Markus Reiterer: Simulation and Computation Related Challenges for the Adoption of In Silico Medicine

##### Abstract:

Patients have continuously increasing expectations for the effectiveness and safety of medical therapies at a time was resources to treat patients are becoming more constraint. The cost of developing improved or new therapies has been continuously rising over the past few decades. In particular the cost of the regulatory process has outpaced the revenue growth of the medical device industry. In silico medicine has the potential to slow down the acceleration of the evidence cost, while at the same time reduce the exposure of patients to unproven therapies, and to improve the efficacy and safety of the devices. In my talk, I will cover at a high level several issues where the application of smart and sophisticated mathematics and computation, including data science is needed to make a difference. There are still many unresolved challenged with creating personalized or individualized computer models of the interaction of a medical device with a patient. Examples are models of diabetic patients, semi-automated workflows for the generation models from medical images, Bayesian approaches to combine human and in silico clinical evidence for regulatory submissions, and literature reviews generated by cognitive computing that result in a treatment recommendation. Markus Reiterer, grow up in Austria and received both his Dipl.-Ing. (M.S.) and Doctorate (Ph.D.) from the University of Leoben in Austria. During his graduate studies, Markus was employed as Research Associate at the Fraunhofer-Institute for Mechanics of Materials in Freiburg, Germany. In 2004 Markus joined Sandia Natl. Labs as Post-doctoral Appointee, where he continued his research in computational simulation of sintering of ceramics. He is an internationally recognized expert in mechanics of granular media and theory of sintering. Since joining Medtronic in 2006, Markus has been subject matter experts in many projects critical to quality or revenue. He is known as expert for FEA of materials with complex behavior, high cycle fatigue, welding and joining, and tribology. Markus serves as information hub for additive manufacturing and has also been leading the Pan-Medtronic Working Group for Modeling and Simulation. Since the first days at Medtronic Markus has been active on the Technical Forum and served on the organizing committee for the annual S&T Conference. Currently, Markus is the President-Elect for the Technical Forum. Markus has been successfully leading several Medtronic - universi

MCFAM Seminar - No Seminar

Student Combinatorics Seminar

Reciprocity and Functoriality

##### Abstract:

I will introduce these two important concepts in Langlands program through examples within GL(n), the general linear group. In particular, I will mention some recent results concerning them

Algebraic Geometry Reading Group Seminar

Some Fully Nonlinear Elliptic Equations in Complex Geometry

##### Abstract:

We consider fully nonlinear elliptic equations on Hermitian manifolds which depend on the gradient in some nontrivial ways. Some of these equations arise from interesting problems in complex geometry, such as a conjecture by Gauduchon which is a natural generalization of Calabi conjecture to the Hermitian setting, and finding balanced metrics on Hermitian manifolds. There are substantial difficulties in deriving a priori estimates for such equations. We discuss some new ideas to overcome these difficulties, and for a special but large class of equations which may be degenerate we can derive all the desired estimates under very general conditions. The talk is based on joint work with Xiaolan Nie, Chunhui Qiu and Rirong Ruan

SIAM Student Chapter Reading Group Seminar

Math Physics Seminar

##### Abstract:

see attached abstract

Math Club

Commutative Algebra Seminar

Noncompact Shrinking 4 Soliton with Nonnegative Curvature (II)

Daniel Onofrei: Field Control Through Manipulation of Surface Sources

##### Abstract:

In this talk we will discuss our past and recent results regarding the problem of electromagnetic field manipulation with the help of active sources situated on exterior surfaces. We will first present a series of smooth scalar control results for the Helmholtz equation and based on these results we will describe our strategy for electromagnetic field control. Applications to scattering cancellation, field synthesis ( in free space and waveguides) and inverse source problems will be discussed as well.

SIAM Student Chapter Reading Group Seminar

Global Smoothness of the Monge-Ampere Eigenfunctions

##### Abstract:

In this talk, I will introduce the Monge-Ampere eigenvalue problem and discuss the global smoothness of the eigenfunctions. The question of global higher derivative estimates up to the boundary of the eigenfunctions of the Monge-Ampere operator is a well known open problem. I will discuss the recent resolution of global smoothness of the eigenfunctions of the Monge-Ampere operator on smooth, bounded and uniformly convex domains in all dimensions. A key ingredient in our analysis is boundary Schauder estimates for certain degenerate Monge-Ampere equations. This is joint work with Ovidiu Savin.

Algebraic Geometry Seminar

The Koch-Tataru Theorem: Well-posedness of the Navier-Stokes Equations in BMO^{-1}

##### Abstract:

We present the results of Herbert Koch and Daniel Tataru on global well-posedness of the Navier-Stokes equations in the critical space BMO^{-1}

Brian Malcolm Brown: Uniqueness for an Inverse Problem in Electromagnetism with Partial Data

##### Abstract:

A uniqueness result for the recovery of the electric and magnetic coefficients in the time-harmonic Maxwell equations from local boundary measurements is shown. No special geometrical condition are imposed on the inaccessible part of the boundary of the domain, apart from that that the boundary of the domain is C1,1. The coefficients are assumed to coincide on a neighborhood of the boundary: a natural property in many applications.

PDE Seminar - TBA

Differential Geometry and Symplectic Topology seminar

Climate Change Seminar

Automorphic Forms & Number Theory [will not meet]

Approximating Functions with Singularities

##### Abstract:

Title: Approximating Functions with Singularities

Khovanov homotopy

##### Abstract:

The Jones polynomial is an invariant of a knot or link, and Khovanov homology is a categorical lift so that the coefficients of the Jones polynomial are ranks of Khovanov homology groups. I'll discuss a refinement of this to a homotopy type due to Lipshitz-Sarkar and Hu-Kriz-Kriz, and discuss ongoing work to refine this to an invariant for tangles.

Tai-Chia Lin: Virial Theorem and Eigenvalue Estimate of Nonlinear Schrödinger Equations

##### Abstract:

The virial theorem is a nice property for the linear Schr\”{o}dinger equation in atomic and molecular physics as it gives an elegant ratio between the kinetic and potential energies and is useful in assessing the quality of numerically computed eigenvalues. If the governing equation is a nonlinear Schr\”{o}dinger equation with power-law nonlinearity, then a similar ratio can be obtained but there seems no way of getting any eigenvalue estimate. It is surprising as far as we are concerned that when the nonlinearity is either square-root or saturable nonlinearity (not a power-law), one can develop a virial theorem and eigenvalue estimate of nonlinear Schr\”{o}dinger (NLS) equations in R2 with square-root and saturable nonlinearity, respectively. Furthermore, the eigenvalue estimate can be used to prove the 2nd order term (which is of order $\ln\Gamma$) of the lower bound of the ground state energy as the coefficient $\Gamma$ of the nonlinear term tends to infinity.

Student Number Theory Seminar

Reading Seminar for Automorphic Forms

Combinatorics Seminar

Lie Theory Seminar

Prediction without Probability: a PDE approach to some Two-Player Games from Machine Learning

##### Abstract:

In the machine learning literature, one approach to "prediction" assumes

that advice is available from a finite number of "experts." The best prediction in

this setting is the one that "minimizes regret", i.e. minimizes the worst-case

shortfall relative to the best performing expert. My talk discusses a particular

problem of this type, which takes the form of a randomized-strategy two-player game.

I'll explain how it can be addressed using ideas from optimal control and partial

differential equations. The main idea is to consider a suitable continuum limit, and

to characterize the value function using a nonlinear PDE. In some special cases, the

value function even has an exact formula. As a consequence, one knows in those cases

exactly how the experts' guidance should be weighted to obtain an optimal result.

This is joint work with Nadejda Drenska.

The entropy power inequality for the Renyi entropy

##### Abstract:

The entropy power inequality, which is fundamental in Information Theory, states that for every independent continuous random vector X,Y in R^n, one has

N(X+Y) \geq N(X) + N(Y).

Here N(X) denotes the entropy power of X, defined as N(X) = e^{\frac{2}{n}h(X)}, where h(X) is the Shannon entropy of X. This inequality has found applications in other fields, such as the concentration of measure phenomenon, and has deep connections with convex geometry.

In this talk, we will see that the entropy power inequality can be extended to the Renyi entropy.

(Based on a joint work with S. Bobkov.)

MCFAM Seminar - No Seminar

Student Combinatorics Seminar

Colloquium

Algebraic Geometry Reading Group Seminar

Symplectic -2 Spheres and the Symplectomorhism Group of Small Rational 4-Manifolds

##### Abstract:

For a rational 4-manifold $M$, reduced symplectic form play a role since any symplectic form on $M$ is symplectomorphic to a reduced one. We give a combinatoric approach and a Lie theoretic approach to describe the normalized reduced cone for a rational 4-manifold $M$, both will be explicitly illustrated. Using this as a guidance, we see the change and persistence of the symplectomorphism group when one deforms the symplectic form.

SIAM Student Chapter Reading Group Seminar

##### Abstract:

11/3/16 Location Change to B60 FordH

Fearful Symmetry

##### Abstract:

Following the writings of popular mathematics writer Ian Stewart, we explore a number of biological and physical manifestations of symmetry. The stripes of a tiger, the hexagonal arrangement of underwater stones, and the splitting of a water droplet are united by the notion of "symmetry-breaking." This was studied extensively by computer scientist Alan Turing and allows us to prove, for example, that a spotted animal can have a striped tail, but not the other way around.

Math Physics Seminar

Commutative Algebra Seminar

Noncompact Shrinking 4 Soliton with Nonnegative Curvature

SIAM Student Chapter Reading Group Seminar

Active manipulation of acoustic and guided waves

##### Abstract:

In this talk we will describe our recent results about the characterization of continuous boundary data on active sources for the approximation of different prescribed field patterns in given exterior (bounded or unbounded) regions of space. We will present the theoretical ideas behind our results as well as numerical simulations with applications in scattering cancellation, field synthesis and inverse source problems.

Algebraic Geometry Seminar

Quasiperiodic solutions of semilinear elliptic equations in $\mathbb{R}^d$

##### Abstract:

I establish sufficient conditions for the existence of solutions of certain nonhomogeneous semilinear elliptic equations defined on $\mathbb{R}^{N+1}$ which are quasiperiodic in one variable and decaying in the other N variables. Such solutions are found using a center manifold reduction and the KAM theory, along with some tools from Hamiltonian systems. Time permitting, I will also explain how the conditions are ``generic'' in some appropriate sense. Joint work with P. Polacik.

Differential Geometry and Symplectic Topology seminar

Climate Change Seminar

Metaplectic Iwahori-Whittaker functions and Demazure-Lusztig operators

##### Abstract:

Demazure-Lusztig operators appear throughout the study of p-adic Whittaker functions. They can be used to construct related objects, in both the nonmetaplectic and the metaplectic, and the finite-dimensional and affine setting. Brubaker, Bump and Licata used them to describe Iwahori-Whittaker functions in the finite-dimensional setting; Manish Patnaik to prove an analogue of the Casselman-Shalika formula for affine Kac-Moody groups.

In this talk, I will review how metaplectic analogues of the classical operators can be used to prove an analogue of Tokuyama's theorem. This links the constructions of Whittaker functions as a sum over a highest weight crystal (Brubaker-Bump-Friedberg and McNamara), and as a sum over a Weyl group (Chinta-Offen and McNamara). Then I will discuss joint work with Manish Patnaik that relates metaplectic Iwahori-Whittaker functions to Demazure-Lusztig operators in the finite dimensional as well as in the affine setting.

Approximating Functions with Singularities

##### Abstract:

Title: Approximating Functions with Singularities

Weyl n-algebras and the Swiss cheese operad

##### Abstract:

I will discuss the definition and applications of Weyl n-algebras and connected algebras over the Swiss cheese operad.

Student Number Theory Seminar

Reading Seminar for Automorphic Forms

Combinatorics Seminar

Lie Theory Seminar

Extended Extremal Process and Friends in Branching Brownian Motion

##### Abstract:

Branching Brownian motion (BBM) is a classical process in probability, describing a population of particles performing independent Brownian motion and branching according to a Galton Watson process. Arguin et al.\ and A\"\i{}d\'ekon et al.\ proved the convergence of the extremal process. In this talk we show how their result can be extended to a two dimensional process by first choosing a suitable embedding of the Galton Watson process (joint with A. Bovier). Then we discuss how this can be used to construct a class of one-dimensional diffusion processes on the particles of BBM that are symmetric w.r.t. the limits of random martingale measures (joint with S. Andres).

Mixed Methods for Two-Phase Darcy-Stokes Mixtures of Partially Melted Materials with Regions of Zero Porosity

##### Abstract:

The Earth's mantle (or, e.g., a glacier) involves a deformable solid matrix phase within which a second phase, a fluid, may form due to melting processes. The system is modeled as a dual-continuum mixture, with at each point of space the solid matrix being governed by a Stokes flow and the fluid melt, if it exists, being governed by a Darcy law. This system is mathematically degenerate when the porosity (volume fraction of fluid) vanishes. Assuming the porosity is given, we develop a mixed variational framework for the mechanics of the system by carefully scaling the Darcy variables by powers of the porosity. We prove that the variational problem is well-posed, even when there are regions of one and two phases (i.e., even when there are regions of positive measure where the porosity vanishes). We then develop an accurate mixed finite element method for solving this Darcy-Stokes system and prove a convergence result. Numerical results are presented that illustrate and verify the convergence of the method.

William Satzer: Desirable Characteristics of a Mathematician in Industry: One Person's View

##### Abstract:

I'll discuss attributes of mathematics Ph.D.s that make them attractive to an employer in industry, as well as some obstacles that mathematics Ph.D.s face. Bill Satzer received a Ph.D. in mathematics from the University of Minnesota under the supervision of Dick McGehee. He recently retired from 3M. Before 3M, he worked in a variety of engineering R&D positions at three other companies.

MCFAM Seminar - No Seminar

Arya Mazumdar: Clustering with an Oracle

##### Abstract:

Given a set V of n elements, consider the simple task of clustering them into k clusters, where k is unknown. We are allowed to make pairwise queries. Given elements u and v in V, a query asks whether u,v belong to the same cluster and returns a binary answer assuming a true underlying clustering. The goal is to minimize the number of such queries to correctly reconstruct the clusters. When the answer to each query is correct, a simple lower and upper bound of Theta(nk) on query complexity is easy to derive. Our major contribution is to show how only a mild side information in the form of a similarity matrix leads to a great reduction in query complexity to O(k^2). This remains true even when the answer of each query can be erroneous with certain probability and `resampling' is not allowed. Note that this bound can be significantly sublinear in n depending on the value of k. We also develop parallel versions of our algorithms which give near-optimal bounds on the number of adaptive rounds required to match the query complexity.

To show our lower bounds we introduce new general information theoretic methods; as well as use, in completely novel way, information theoretic inequalities to design efficient algorithms for clustering with near-optimal complexity. We believe our techniques both for the lower and upper bounds are of general interest, and will find many applications in theoretical computer science and machine learning. This talk is based on a joint work with Barna Saha.

Arya Mazumdar is an assistant professor in the College of Information and Computer Sciences at the University of Massachusetts Amherst. Prior to this, Arya was an assistant professor at University of Minnesota-Twin Cities, and form Aug 2011 to Dec 2012, he was a postdoctoral scholar at Massachusetts Institute of Technology. Arya received his Ph.D. from University of Maryland, College Park, in 2011. Arya is a recipient of the 2014-15 NSF CAREER award and the 2010 IEEE ISIT Jack K. Wolf Student Paper Award. He is also a recipient of the Distinguished Dissertation Fellowship Award, 2011, at the University of Maryland. He spent the summers of 2008 and 2010 at the Hewlett-Packard Laboratories, Palo Alto, CA, and IBM Almaden Research Center, San Jose, CA, respectively. Arya's research interests include information theory, coding theory, and their applications to CS theory/learning.

Student Combinatorics Seminar

Feynman Categories: Definition and Applications

##### Abstract:

Feynman categories are a novel framework generalizing groups, algebras, substitution schemes, etc. as they appear in geometry, topology, number theory and mathematical physics. We start with the definition and basic examples including set theoretic examples and examples of graphs, such as Feynman graphs or those appearing in operad like theory. We then move on to give several constructions and secondary structures. These include resolutions, model category structure as well as Hopf algebras. The latter are a secondary structure that appears for instance in the theory of multi-zeta values, renormalization and double loop spaces.

Algebraic Geometry Reading Group Seminar

SIAM Student Chapter Reading Group Seminar

Foliations of Contact Manifolds by Planar Pseudoholomorphic Curves and the Weinstein Conjecture

##### Abstract:

In this talk, we will describe foliations of high dimensional “iterated planar" contact manifolds by pseudoholomorphic curves and show that, by using this kind of technology, one can prove the long-standing Weinstein conjecture for iterated planar contact manifolds.

Math Club

Math Physics Seminar

The Local Cohomology of FI-modules

##### Abstract:

Much of the work in homological invariants of FI-modules has been concerned with properties of certain right exact functors. One reason for this is that the category of coherent FI-modules over a commutative ring very rarely has sufficiently many injectives. In this talk, we consider the (left exact) torsion functor on the category of coherent FI-modules, and show that its derived functors exist. Properties of these derived functors, which we call the local cohomology functors, can be used in reproving well known theorems relating to the depth, regularity, and stable range of a module. We will see that various facts from the local cohomology of modules over a polynomial ring have analogs in our context. We will also see that there is a way to make sense of a kind of local duality for FI-modules. This is largely joint work with Liping Li.

Geometry of Gradient Shrinking Ricci solitons (II)

Junshan Lin: Scattering and Field Enhancement of Subwavelength Slits

##### Abstract:

Subwavelength apertures and holes on surfaces of metals induce strong electromagnetic field enhancement and extraordinary optical transmission. This remarkable phenomenon can lead to potentially significant applications in biological and chemical sensing, spectroscopy, and other novel optical devices. In this talk, I will present mathematical studies of the enhancement mechanism for the scattering of narrow slits in a slab of perfect conductor. Both the single slit and an array of slits will be discussed. It is demonstrated that the enhancement of the electromagnetic field for a single slit can be induced either by Fabry-Perot type scattering resonances or certain non-resonant effect in the low frequency. We derive the asymptotic expansions of resonances and quantitatively analyze the field enhancement at resonant frequencies. The field enhancement at non-resonant frequencies in the low frequency is also investigated, and it is shown that the fast transition of the magnetic field in the slit induces strong electric field enhancement. For a periodic array of slits, we show that additional enhancement mechanisms arise when the size of period changes.

SIAM Student Chapter Reading Group Seminar

The influence of a line of fast diffusion on KPP propagation: nonlocal exchanges

##### Abstract:

The purpose of this talk is to present some results concerning the effects of nonlocal exchanges between a line of fast diffusion and a two-dimensional environment in which standard reaction-diffusion occurs. The initial model was introduced in 2013 by Berestycki, Roquejoffre, and Rossi. We present how the coupling enhances the spreading in the direction of the line, and what may be the influence of nonlocal exchanges on the spreading velocity.We also investigate the singular limits of infinitely supported exchanges or exchanges that tend to Dirac masses.

Algebraic Geometry Seminar

Hamiltonian systems and KAM theory

##### Abstract:

The Kolmogorov-Arnold-Moser (KAM) theory is an important tool to obtain quasiperiodic solutions for Hamiltonian systems. In this talk I will introduce basic concepts of Hamiltonian systems, explain how the KAM theory is applied, and some tools allowing one to set up a Hamiltonian system in a suitable form for the KAM theory.

Maxence Cassier: Spectral Theory and Limiting Amplitude Principle for Maxwell’s Equations at the Interface of a Metamaterial

##### Abstract:

In this talk, we are interesting in a transmission problem between a dielectric and a metamaterial. The question we consider is the following: does the limiting amplitude principle hold in such a medium? This principle defines the stationary regime as the large time asymptotic behavior of a system subject to a periodic excitation. An answer is proposed here in the case of a two-layered medium composed of a dielectric and a particular metamaterial (Drude model). In this context, we reformulate the time-dependent Maxwell’s equations as a Schrödinger equation and perform its complete spectral analysis. This permits a quasi-explicit representation of the solution via the ”generalized diagonalization” of the associated unbounded self-adjoint operator. As an application of this study, we show finally that the limiting amplitude principle holds except for a particular frequency, called the plasmonic frequency, characterised by a ratio of permittivities and permeabilities equal to ?1 across the interface. This frequency is a resonance of the system and the response to this excitation blows up linearly in time.

On ancient solutions of the Navier-Stokes equations III

Differential Geometry and Symplectic Topology seminar

Diana Negoescu: Differentiated HIV Viral Load Monitoring in Resource Limited Settings: An Economic Analysis

##### Abstract:

Viral load (VL) monitoring for patients receiving antiretroviral therapy (ART) is recommended worldwide. However, the costs of frequent monitoring are a barrier to implementation in resource-limited settings. The extent to which personalized monitoring frequencies may be cost-effective is unknown. We created a simulation model parameterized using person-level longitudinal data to assess the benefits of flexible monitoring frequencies. Our data-driven model tracked HIV+ individuals for 10 years following ART initiation. We then optimized the interval between viral load tests as a function of patients’ age, gender, education, duration since ART initiation, adherence behavior, and the willingness-to-pay threshold. We compared the cost-effectiveness of the personalized monitoring strategies to fixed monitoring intervals every 1, 3, 6, 12 and 24 months. We find that focusing on patients most at risk of virological failure improves the efficiency of VL monitoring. In low- and middle-income countries, adaptive policies achieve similar outcomes to fixed interval at lower costs, while in high-income countries adaptive policies can outperform fixed policies both in terms on health benefits and costs.

Diana Negoescu is an Assistant Professor in the Industrial and Systems Engineering Department at the University of Minnesota. Her broad research interest lie in the application of operations research and management science to medical and health policy decision-making problems. In particular, her research focuses on personalized medical decision-making and healthcare models for problems where patient characteristics are partially unknown or evolving over time, and where decision makers are risk-averse, or face constraints on the resources they can use or the actions they can take.

Climate Change Seminar

[postponed]

Approximating Functions with Singularities

##### Abstract:

Title: Approximating Functions with Singularities

Affinization, Witt vectors and duality

##### Abstract:

The Hochschild--Kostant--Rosenberg theorem relates the Hochschild homology and Andre--Quillen homology of smooth commutative algebras. Using ideas from derived algebraic geometry, Ben-Zvi--Nadler proved an HKR theorem for

rational E_\infty-rings sans smoothness hypotheses. Their argument ultimately relies on an equivalence between the algebra of rational cochains on the circle and a trivial square-zero extension. We will explain how the situation is more complicated away from characteristic zero, and why this is actually a good thing.

Student Number Theory Seminar

Reading Seminar for Automorphic Forms

Correlation: A Biography of Dangerous Ideas, Implications for Big-Data Practitioners

##### Abstract:

More and more data analysts, scientists & artists are embracing the revelation of the renewed Big-Data Analytics Trinity: Volume, Variety & Velocity Correlations and associations have been a cornerstone of scientific data analysis since birth providing mixed blessings and unintended curses Playing an important role in areas such: assets pricing, simulating risk and variables selection model optimization and recommender systems, old malaises in the Big-Data era require no less if not more attention The suggested light presentation will provide review of correlation concepts and use, illustrates caveats and demonstrates alternatives developed to correlations.

Bio: Dr. Carmel Nadav holds a PhD in Applied Economics from the University of Minnesota and an MSc and BSc in Agricultural and Applied Economics from the Hebrew Univeristy, Israel. Carmel has more than 11 years of experience working in the U.S. Banking Sector in the areas of forecasting and marketing. Prior to joining Wells Fargo Bank, Carmel worked as a consultant in a variety of firms including: Consumer Packaged Goods (Sears Forecasting, Duracell Marketing Mix), Energy Pricing and Forecasting (TXU Energy, PJM Regional Transmission Organization), Consumer Insights (GM OnStar, Sprint, National City Bank, Wells Fargo) and Credit (Sears Credit).

Carmel's interests span from Markovian models to advanced text analytics problems. His work emphasizes insights from real world data packaged with analytics and reporting to provide meaningful business solutions.

K-Theory and Monodromy of Schubert

##### Abstract:

I will describe the combinatorics of Schubert curves, which are one-dimensional Schubert problems defined with respect to flags osculating the rational normal curve. The real geometry of such curves is described by orbits of a map $\omega$ on skew tableaux, defined as the commutator of jeu de taquin rectification and promotion. In particular, the real locus of the Schubert curve naturally covers $RP^1$, with $\omega$ as the monodromy operator.

I will give a local, faster algorithm for computing $\omega$ without rectifying the tableau. Certain steps in the algorithm are in bijection with Pechenik and Yong's 'genomic tableaux', which enumerate the K-theoretic Littlewood-Richardson coefficient of the Schubert curve. As a corollary, I'll give purely combinatorial proofs of several numerical results relating the K-theory and real geometry of the curve. This is joint work with Maria Monks Gillespie.

Lie Theory Seminar

Sensitivity analysis of the expected utility maximization problem with respect to perturbations of the market price of risk

##### Abstract:

We will consider Merton’s portfolio problem in various formulations and methods of solutions. We will also describe several no-arbitrage conditions and the validity of the key assertions of the utility maximization theory under them.

Then, in the framework of an incomplete financial market where the stock price dynamics is modeled by a continuous semimartingale, we will provide an explicit second-order expansion formula for the power investor’s value function seen as a function of the underlying market price of risk process. Finally, we will establish a first-order approximation of the optimal wealth process and illustrate this result by an example.

Efficient Spectral Methods for Solving a Class of Fractional PDEs

##### Abstract:

We consider spectral approximations of fractional PDEs in bounded and unbounded domains.

For fractional PDEs based on Riemann-Liouville or Caputo derivatives in bounded domains, two main difficulties are:

(i) they are non-local operators; and (ii) they lead

to singular solutions at domain boundaries. We introduce

a family of generalized Jacobi functions (GJFs) such that their fractional derivatives can be easily computed, and present spectral methods which are as efficient as the spectral methods for regular PDEs.

We also present error estimates which show that spectral convergence rate in properly weighted Sobolev spaces can be achieved despite the fact that the solutions have singularities at the endpoints. For fractional PDEs based on fractional Laplacians in unbounded domains, the solutions decay very slowly at infinity and no transparent boundary condition is available for domain truncation, we develop efficient spectral-collocation and spectral-Galerkin methods using Hermite functions to solve thes problems in unbounded domains directly.

Student Combinatorics Seminar

Recent Progress in Periodic and Almost-Periodic Homogenization

##### Abstract:

In this talk I will discuss some of the recent progress on quantitative homogenization in the periodic and almost-periodic settings. We consider a family of second-order elliptic systems with rapidly oscillating periodic or almost-periodic coefficients, arising in the theory of homogenization. The results to be presented include boundary Lipschitz estimates, Rellich estimates, estimates of approximate correctors, and convergence rates.

On ancient solutions of the Navier-Stokes equations II

Algebraic Geometry Reading Group Seminar

SIAM Student Chapter Reading Group Seminar

Differential Geometry and Symplectic Topology seminar

Math Club

Math Physics Seminar

Commutative Algebra Seminar

Geometry of Gradient Shrinking Ricci solitons

Eduard-Wilhelm Kirr: Can one find all coherent structures of a nonlinear wave equation?

##### Abstract:

Coherent structures are special solutions of a given wave equation which are usually localized and propagate without changing shape. They play an essential role not only in applications but also in the theory of wave propagation where it is believed that any initial data evolves into a superposition of coherent structures (asymptotic completeness conjecture). While the answer to the title question is still no, except for the rare integrable systems, I will present recent progress

in this direction based on both local and global bifurcation theory.

SIAM Student Chapter Reading Group Seminar

Global weak solutions to Cauchy for the Navier-Stokes equations for initial data outside of the energy class

##### Abstract:

In the talk, I'll discuss a definition and global existence of weak

solutions to the Cauchy problem for the Navier-Stokes equations with

initial data belonging to critical spaces such as $L_3$ or weak $

L_3$. Those initial data generically have infinite energy. However,

the construction of weak solutions is such that they are in a sense

still "energy" solutions. To be more precise, the difference between

a weak solution and the heat semigroup generated by the same initial

data has a finite energy in Leray's sense. Moreover, weak solutions

satisfy the local energy inequality and thus the Caffarelli-Kohn-Nirenberg theory is applicable to them. Uniqueness and regularity issues are going to be discussed as well.

Algebraic Geometry Seminar

Spectral Methods in Matlab

##### Abstract:

In many scenarios (like fluid dynamics), one reduces a problem by adding the constraint of periodicity. This constraint leads to so-called "spectral methods," numerical schemes with exponential rates of convergence. The idea is simple: reduce the PDE to an infinite dimensional ODE in Fourier space and then solve the ODE using standard techniques. In practice, the process is more difficult when we use a finite dimensional approximation. In these two talks, I will discuss the theory and implementation of a basic spectral method for Burgers equation in Matlab. The first lecture will cover the general theory and approach (with Matlab examples), while the second lectuer will discuss an issue specific to spectral methods: de-aliasing. After my two presentations, you will have learned the "why and how" of spectral methods in Matlab.

Peter Monk: Tutorial: Convolution Quadrature and Maxwell’s Equations

Differential Geometry and Symplectic Topology seminar

Climate Change Seminar

Approximating Functions with Singularities

##### Abstract:

Title: Approximating Functions with Singularities

POSTPONED

Topological Hochschild homology of (some) perfectoid fields

##### Abstract:

Beside its familiar topology, the field of complex numbers has complete

p-adic topologies for all integral primes. Unlike the Archimedean topology, which has only the real numbers as a complete topological

subfield, the p-adic topologies have many interesting

(complete, totally ramified) subfields: in particular, the completions

of maximal totally ramified extensions of locally compact

number fields (such as the p-cyclotomic field obtained by adjoining

all p-power roots of unity to the p-adic rationals).

Recent work of Scholze, Bhatt and others has transformed the study of

algebraic geometry over such fields, while similarly recent work of

Hesselholt and Madsen has transformed our understanding of their algebraic

topology. This talk will focus on connections between Lubin-Tate (ie generalized cyclotomic field) theory and topological Hochschild homology,

which seems to be a powerful tool for understanding perfectoid geometry.

Student Number Theory Seminar

Peter Monk: Tutorial: Convolution Quadrature and Time Domain Integral Equations

Reading Seminar for Automorphic Forms

MCFAM Seminar - No Seminar

Ordered set partitions, generalized coinvariant algebras, and the Delta Conjecture.

##### Abstract:

Consider the action of the polynomial ring $\mathfrak{S}_n$ on the polynomial ring $\mathbb{Q}[x_1, \dots, x_n]$ by variable permutation. The {\em coinvariant algebra} $R_n$ is the graded $\mathfrak{S}_n$-module obtained by modding out $\mathbb{Q}[x_1, \dots, x_n]$ by the ideal generated by $\mathfrak{S}_n$-invariant polynomials with vanishing constant term. The algebraic properties of $R_n$ are governed by the combinatorial properties of permutations. We will introduce and study a family of graded $\mathfrak{S}_n$-modules $R_{n,k}$ which depend on two positive integers $k \leq n$ which reduce to the coinvariant algebra when $k = n$. The algebraic properties of the $R_{n,k}$ are governed by ordered set partitions of $\{1, 2, \dots, n\}$ with $k$ blocks. We will generalize results of E. Artin, Garsia-Stanton, Chevalley, and Lusztig-Stanley from $R_n$ to $R_{n,k}$. The modules $R_{n,k}$ are related to the {\em Delta Conjecture} in the theory of Macdonald polynomials. Joint with Jim Haglund and Mark Shimozono.

Lie Theory Seminar

Threshold Dynamics for Multiphase, Anisotropic Mean Curvature Motion

##### Abstract:

Motion by mean curvature of networks of surfaces arises in many applications, including computer vision (in the context of the Mumford-Shah segmentation model) and materials science (in the context of Mullins’ model for grain networks in polycrystalline materials). It describes gradient flow for a cost function that measures the surface area of interfaces that partition a domain into disjoint regions. Junction conditions that stipulate behavior along curves where three of more surfaces may meet, along with inevitable topological changes to the network, make computing these evolutions particularly challenging. Anisotropic versions of the flow, where the corresponding cost function is a normal dependent version of surface area, are of great interest in the materials science context.

In 1989, Merriman, Bence, and Osher proposed an elegant algorithm known as threshold dynamics that approximates this evolution in the simplest two-phase, isotropic setting. It generates the approximation simply by alternating two efficient operations: Convolution, and thresholding. Since then, much has been written on whether such a simple algorithm can be extended, while maintaining its simplicity and efficiency, to (1) arbitrary networks, and (2) anisotropic surface energies. Even the two-phase, anisotropic situation remained unsolved. Drawing on a recent variational formulation of threshold dynamics (joint work with Felix Otto), we will give a fairly complete answer to the fully anisotropic, multiphase question.

Based on joint works with Matt Elsey, Matt Jacobs, and Pengbo Zhang.

Estimating Rare Event Probabilities in Reflecting Brownian Motion

##### Abstract:

In this talk I will broadly discuss the use of particle methods for the estimation of rare event probabilities. In particular, I will discuss the so-called 'splitting method' and what conditions are necessary to ensure a stable and efficient algorithm. I will then discuss how this algorithm can be used for estimating rare event probabilities in the specific case of reflecting Brownian motion.

Viktoria Averina: Things I’ve learned from 10 years in industry

##### Abstract:

A collage of stories and lessons from working in biomedical research on implantable cardiac devices and why I found it more rewarding than the academic career option. About the speaker: I was born in Russia into a family and in fact a whole city of scientists. I remember deciding to be a teacher when I was 7. My life seem to have zigzagged between science and teaching ever since. After graduation with a BS in math and physics education in 2000, a random turn of events landed me in the middle of freakishly cold nowhere, aka University of Alaska Fairbanks. I earned MS in pure mathematics there and moved on to a 9-month stint in Knox College Illinois as a visiting instructor of mathematics. Despite my disappointments with the realities of teaching, I continued my pursuit of the academic career path and entered the Applied Math PhD program at University of Minnesota in 2003. As part of exploring the “applied” side of the program and in search of the problem for the dissertation, I found an industrial internship at Guidant (now Boston Scientific). From day one, I was captivated by how many unsolved mysteries our bodies and diseases hold. The experiences of that three-month internship have shifted my career path from academy to industry. And the decision to accept full-time research scientist position while still in school has transformed my life to rewarding but at many times hellish ride. Now, 10 years post that decision, I am a principal research scientist at Boston Scientific who authored dozens of patents and, more rewardingly, many features that are enabled in thousands of implantable devices across the world, helping people live better and longer lives. I have also earned my PhD in applied math with cardiovascular physiology minor and, surprisingly, with most of my psyche still intact. Ironically, I am back to teaching again in small doses, when transferring research knowledge to our marketing and sales forces

Student Combinatorics Seminar

Colloquium

Algebraic Geometry Reading Group Seminar

SIAM Student Chapter Reading Group Seminar

Differential Geometry and Symplectic Topology seminar

Math Physics Seminar

Math Club

Commutative Algebra Seminar

Hessian Equations on closed Hermitian Manifolds

Roy Goodman: Bifurcations of Long-Lived (near) Relative Periodic Orbits in Coupled Nonlinear Waveguides

##### Abstract:

We consider the nonlinear propagation of light along an array of two or three coupled waveguides. The three waveguide system is known to support nine different stationary time-harmonic solutions. We apply a bag of tricks from Hamiltonian mechanics to understand non-trivial time-periodic solutions in which light moves periodically among the three wells and find a variety of bifurcations and other surprising behaviors.

SIAM Student Chapter Reading Group Seminar

Regularity of solutions in semilinear elliptic theory

##### Abstract:

We present regularity results for the classical semilinear elliptic equation \Delta u = f(x,u) in B_1 and discuss several associated free boundary problems. The techniques are self-contained and involve an L^2 projection operator. Based on joint work with Minne and Nurbekyan.

Algebraic Geometry Seminar

Spectral Methods in Matlab

##### Abstract:

In many scenarios (like fluid dynamics), one reduces a problem by adding the constraint of periodicity. This constraint leads to so-called "spectral methods," numerical schemes with exponential rates of convergence. The idea is simple: reduce the PDE to an infinite dimensional ODE in Fourier space and then solve the ODE using standard techniques. In practice, the process is more difficult when we use a finite dimensional approximation. In these two talks, I will discuss the theory and implementation of a basic spectral method for Burgers equation in Matlab. The first lecture will cover the general theory and approach (with Matlab examples), while the second lectuer will discuss an issue specific to spectral methods: de-aliasing. After my two presentations, you will have learned the "why and how" of spectral methods in Matlab.

On ancient solutions of the Navier-Stokes equations I

Matteo Convertino: The Population Connectome: Information Theoretical Models for Predicting and Controlling Population Patterns

##### Abstract:

Traditional mechanistic models have tried to dissect the complexity of complex biological and socio-environmental processes. However, because of the boom in data, the need of simplified models, and the recognition of emerging collective-behavior driven patterns, complexity science has raised as the science to purposely decrease the complexity of complex systems by inferring their fundamental processes and providing useful and usable models.

The talk will introduce information theoretic models to infer the functional and structural networks - i.e. the "population connectome" - underlying processes leading to complex population patterns. The nature inspired model simulates dynamical processes on complex networks in a Lagrangian framework after learning from data the necessary and sufficient information to reproduce patterns of interests. The model will highlight forecasting and management studies about public health issues related to endemic, epidemic and pandemic infectious diseases (influenza, dengue, and cholera for instance). The utility of the model at smaller socio-biological scales will be shown for population-driven personalized medicine and biological investigation (e.g. for understanding and forecasting pain and identifying biomarker networks).

Despite the engineering bias for a systemic epidemiology roadmap, the talk will underline the ability of models to determine universality and scale invariance of population patterns via topological analyses. Reverse engineering uses of the model for multiscale system design, technology fabrication, experiment planning and health/biomedical investigations will be shown.

Dr. Convertino is a MnDRIVE Assistant Professor in the School of Public Health, Division of Environmental Health Sciences and Public Health Informatics Program, at the University of Minnesota. At the same institution he is also Faculty Fellow at the Institute on the Environment, Institute for Engineering in Medicine, and at the Bioinformatics and Computational Biology Program. He is actively involved in the Risk Unit of the Center for Animal Health and Food Safety, and in the Ecosystem Health Division both of the College of Veterinary Medicine at the University of Minnesota. Internationally he is a Foreign Fellow of the International Institute for Applied Systems Analysis (IIASA) in Vienna, Austria.

Dr. Convertino has been trained in Civil and Environmental Engineering (Structural & Environmental Engineering majors) for the Bache

Differential Geometry and Symplectic Topology seminar

Climate Change Seminar

POSTPONED

Approximating Functions with Singularities

##### Abstract:

Title: Approximating Functions with Singularities

Goodwillie calculus and Mackey functors

##### Abstract:

This talk concerns a theorem stating that the theory of n-excisive functors from the category of spectra to a target stable oo-category E is equivalent to the theory of Mackey functors on a suitable indexing category - the category of finite sets of cardinality at most n with morphisms surjections - which has many of the salient properties of the orbit category of a finite group. We'll give motivation for this theorem, and give a broad sketch of the proof, which decomposes readily into a sequence of independent assertions. We'll then prove as many of these assertions as time allows.

Student Number Theory Seminar

Reading Seminar for Automorphic Forms

Daily life of Data at a Large Retailer

##### Abstract:

This talk, given by one of Target's Senior Lead Data Scientists, Dr. Jesse Berwald, follows the data life cycle of a large retailer, from data ingestion to product output. The analysis tools - from Python, Spark, and Hive to old fashioned mathematics; the data leveraged - from in-store sales records and click stream behavior to natural language documents; and finally, the algorithms utilized.

Bio: As part of a team at Target with deep industry knowledge Dr. Berwald develops best-in-class machine learning algorithms in an omnichannel environment. His work involves predictive analytics, natural language processing, deep learning for visual and text sentiment analysis, topological data analysis, and old-fashioned data wrangling using a full, open-source stack. Prior to joining Target Dr. Berwald held many research positions including: Post Doctoral Fellow at the Institute for Mathematics and its Applications (IMA) Post Doctoral Researcher at the College of William and Mary, graduate research and teaching positions at Montana State University at Bozeman, Sandia National Laboratories and Los Alamos National Laboratories. He also worked at IBM for three years as a software engineer. Dr. Berwald got his PhD in Mathematics from Montana State University at Bozeman and his BS in Mathematics at the University of Michigan, Ann Arbor.

Zamolodchikov Periodicity and Integrability

##### Abstract:

We call a quiver Zamolodchikov periodic (resp.,

Zamolodchikov integrable) if the values of the associated $T$-system at each vertex are periodic (resp., satisfy a linear recurrence). It has been shown by Keller that quivers obtained as products of two Dynkin diagrams are Zamolodchikov periodic. We prove that a quiver is Zamolodchikov periodic if and only if it admits a strictly subadditive labeling. Next, we show that if a quiver is Zamolodchikov integrable, then it admits a subadditive labeling. We classify all quivers

admitting a subadditive or a strictly subadditive labeling. Finally, we concentrate on the quivers of type $\hat A \otimes A$. In this case, we express the coefficients of the recurrences in terms of the partition functions for domino tilings of a cylinder. This is joint work with Pavlo Pylyavskyy.

Lie Theory Seminar

Afonso Bandeira: Optimality and Sub-optimality of Principal Component Analysis for Spiked Random Matrices

##### Abstract:

A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector (or low rank structure) is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences, where the goal is often to recover or detect the planted low rank structured. In this talk we discuss fundamental limitations of statistical methods to perform these tasks and methods that outperform PCA at it. Emphasis will be given to low rank structures arising in Synchronization problems.

Optimality and Sub-optimality of Principal Component Analysis for Spiked Random Matrices

##### Abstract:

A central problem of random matrix theory is to understand

the eigenvalues of spiked random matrix models, in which a prominent

eigenvector (or low rank structure) is planted into a random matrix.

These distributions form natural statistical models for principal

component analysis (PCA) problems throughout the sciences, where the

goal is often to recover or detect the planted low rank structured. In

this talk we discuss fundamental limitations of statistical methods to

perform these tasks and methods that outperform PCA at it. Emphasis

will be given to low rank structures arising in Synchronization

problems.

Collective Cell Motion in Biology

##### Abstract:

The phenomenon of collective cell motion is widespread in biology. Cells move as individuals, as loosely signalling groups, as units in a sheet, etc. In this talk I will

review a number of applications in normal development and disease. The modelling approaches will range from partial differential equations to hybrid discrete cell-based and particular applications will cover cranial neural crest cell migration, the role of heterogeneity in cancer cell migration and epithelial sheet dynamics.

Student Combinatorics Seminar

Colloquium

Algebraic Geometry Reading Group Seminar

SIAM Student Chapter Reading Group Seminar

Differential Geometry and Symplectic Topology seminar

Should you go to graduate school? (Panel)

##### Abstract:

Come join us for a discussion about graduate schools. Hear from people with a variety of backgrounds discuss their experiences. Pizza and Pop as always!

Commutative Algebra Seminar

Sectional Curvature for Riemannian Manifolds with Density

Graeme Milton: Analytic and Polynomial Materials

##### Abstract:

The theory of inhomogeneous analytic and polynomial materials is developed. These are media where the coefficients entering the equations involve analytic functions or polynomials. Three types of analytic or polynomial materials are identified. The first two types involve an integer p. If p takes its maximum value then we have a complete analytic or polynomial material. Otherwise it is incomplete analytic or polynomial material of rank p. For two-dimensional materials further progress can be made in the identification of analytic and polynomial materials by using the well-known fact that a 90 degrees rotation applied to a divergence free field in a simply connected domain yields a curl-free field, and this can then be expressed as the gradient of a potential. Other exact results for the fields in inhomogeneous media are reviewed. Also reviewed is the subject of metamaterials, as these materials provide a way of realizing desirable coefficients in the equations.

SIAM Student Chapter Reading Group Seminar

Analytic torsion of manifolds with fibered cusps

##### Abstract:

Analytic torsion is a spectral invariant of the Hodge Laplacian of a manifold with a flat connection. On a closed manifold it is equal to a topological invariant known as Reidemeister torsion. I will describe joint work with Frédéric Rochon and David Sher establishing a topological expression for the analytic torsion of a manifold with fibered cusp ends (such as a locally symmetric space of rank one). We establish our result by controlling the behavior of the spectrum along a degenerating class of Riemannian metrics

Newton-Okounkov Bodies of Bott-Samelson and Peterson Varieties

##### Abstract:

The theory of Newton-Okounkov bodies can be viewed as a generalization of the theory of toric varieties; it associates a convex body to an arbitrary variety (equipped with auxiliary data). Although initial steps have been taken for formulating geometric situations under which the

Newton-Okounkov body is a rational polytope, there is much that is still unknown. In particular, very few concrete and explicit examples have been computed thus far. In this talk I will introduce the theory of Newton-Okounkov bodies, and will discuss the construction of Newton-Okounkov bodies of

Peterson and Bott-Samelson varieties (for certain classes of auxiliary data on these varieties). Both of these varieties arise, for instance, in the geometric study of representation

theory.

Sang-Hyun Oh: Tutorial on Plasmonics

Udayan Kanade: Could a Theorem Light Our Lives?

##### Abstract:

When faced with two objectives to maximize, engineers expect a trade-off. In the lighting industry, for example, one wishes to maximize the efficiency of a light source, and also the uniformity of its illumination. Almost all engineers will tell you, without any further thought, that there will be a trade-off between the two. Light source designers have come to live with this trade-off, and write many papers on how to measure and co-optimize these, and other measures of light sources. Enter, a new theorem. We will show that (under certain conditions) this trade-off vanishes: both uniformity and efficiency can be fully optimized. In other words, there is a light source which is as efficient as a light source can be, and as uniform as a light source can be. We will also describe our attempts at creating actual light sources using the new theory, and certain "exotic" side-effects.

Differential Geometry and Symplectic Topology seminar

Climate Change Seminar

Approximating Functions with Singularities

##### Abstract:

Title: Approximating Functions with Singularities

Epstein zeta functions IV

An overview of equivariant stable homotopy theory and stable functor calculus

##### Abstract:

This will be an almost totally expository introduction to certain topics in stable homotopy theory. I'll attempt to motivate and introduce Elmendorf's theorem on G-spaces and the spectral Mackey functor approach to G-spectra. I'll then discuss Goodwillie's functor calculus for functors from spectra to spectra, which answers the question of what it means for such a functor to be "polynomial". If time permits, I'll start exploring the analogies between these two theories, a task which will be taken to its conclusion in next week's talk.

Student Number Theory Seminar

Reading Seminar for Automorphic Forms

Price Optimization in Property & Casualty Insurance

##### Abstract:

Price Optimization is a hot topic in the United States Property/Casualty insurance industry. Just in the past few months, the National Association of Insurance Commissioners issued a white paper, multiple states’ insurance regulators released bulletins, and the Casualty Actuarial Society added it to its Exam 6-US syllabus. The regulatory landscape is quickly changing in regards to the definition of and rules around the usage of Price Optimization in insurance. In this presentation, the speaker will provide a simple example of Price Optimization, give a brief overview of the evolution of Price Optimization discussions within the insurance industry, and discuss the recent regulatory response.

Bio: ?Rick Sutherland is a Fellow of the Casualty Actuarial Society (FCAS). He has worked at the Travelers Company, Inc. for 10 years. Currently he is a 2nd VP in the Business Insurance Product Analytics & Innovation Group within the Umbrella & Professional Lines business unit. His previous positions include: Commercial Accounts-Actuarial, Public Sector-Actuarial and Corporate-Actuarial. He graduated from St. Olaf College with a Bachelor's Degree in Mathematics.

Mathematical Challenges Arising from Modelling in Biology

Discrete Solitons in Infinite Reduced Words

##### Abstract:

We consider a discrete dynamical system where the roles of the states and the carrier are played by translations in an affine Weyl group of type A. The Coxeter generators are enriched by parameters, and the interactions with the carrier are realized using Lusztig's braid move (a,b,c)?(bc/(a+c),a+c,ab/(a+c)). We use wiring diagrams on a cylinder to interpret chamber variables as ?-functions. This allows us to reduce to the discrete Kadomtsev-Petviashvili equation, and thus to obtain N-soliton solutions. This is joint work with Max Glick.

Lie Theory Seminar

Vector diffusion maps and the graph connection Laplacian

##### Abstract:

Vector diffusion maps (VDM) is a mathematical framework for organizing and analyzing high-dimensional datasets that generalizes diffusion maps and other nonlinear dimensionality reduction methods, such as LLE, ISOMAP, and Laplacian eigenmaps. Whereas weighted undirected graphs are commonly used to describe networks and relationships between data objects, in VDM each edge is endowed with an orthogonal transformation encoding the relationship between the data at its vertices. The graph structure and orthogonal transformations are summarized by the graph connection Laplacian. In manifold learning, VDM can infer topological properties from point cloud data such as orientability, and graph connection Laplacians converge to their manifold counterparts (Laplacians for vector fields and higher order forms) in the large sample limit. The graph connection Laplacian satisfies a Cheeger-type inequality that provides a theoretical performance guarantee for the popular spectral algorithm for rotation synchronization, a problem with many applications in robotics and computer vision. The application to 2D class averaging in cryo-electron microscopy will serve as our main motivation.

No seminar

Amit Singer: Vector Diffusion Maps and the Graph Connection Laplacian

##### Abstract:

Vector diffusion maps (VDM) is a mathematical framework for organizing and analyzing high-dimensional datasets that generalizes diffusion maps and other nonlinear dimensionality reduction methods, such as LLE, ISOMAP, and Laplacian eigenmaps. Whereas weighted undirected graphs are commonly used to describe networks and relationships between data objects, in VDM each edge is endowed with an orthogonal transformation encoding the relationship between the data at its vertices. The graph structure and orthogonal transformations are summarized by the graph connection Laplacian. In manifold learning, VDM can infer topological properties from point cloud data such as orientability, and graph connection Laplacians converge to their manifold counterparts (Laplacians for vector fields and higher order forms) in the large sample limit. The graph connection Laplacian satisfies a Cheeger-type inequality that provides a theoretical performance guarantee for the popular spectral algorithm for rotation synchronization, a problem with many applications in robotics and computer vision. The application to 2D class averaging in cryo-electron microscopy will serve as our main motivation.

Sang-Hyun Oh: Tutorial on Plasmonics

Student Combinatorics Seminar

Amit Singer: The Mathematics of Cryo-electron Microscopy

##### Abstract:

Single particle cryo-electron microscopy (EM) recently joined X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy as a high-resolution structural method for biological macromolecules. In single particle cryo-EM, the 3-D structure needs to be determined from many noisy 2-D projection images of individual, ideally identical frozen-hydrated macromolecules whose orientations and positions are random and unknown.

I will give a brief introduction to the modern computational challenges in single particle cryo-EM, focusing on 3-D ab-initio modelling, and how it can be solved using representation theory, Fourier analysis, and semidefinite programming.

The mathematics of cryo-electron microscopy

##### Abstract:

Single particle cryo-electron microscopy (EM) recently joined X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy as a high-resolution structural method for biological macromolecules. In single particle cryo-EM, the 3-D structure needs to be determined from many noisy 2-D projection images of individual, ideally identical frozen-hydrated macromolecules whose orientations and positions are random and unknown. I will give a brief introduction to the modern computational challenges in single particle cryo-EM, focusing on 3-D ab-initio modelling, and how it can be solved using representation theory, Fourier analysis, and semidefinite programming.

Algebraic Geometry Reading Group Seminar

Non-displaceablity of Lagrangian Submanifolds

SIAM Student Chapter Reading Group Seminar

Math Club

Free Complexes on Smooth Toric Varieties

##### Abstract:

Given a module M over the Cox ring S of a smooth toric variety, one can consider free complexes that are acyclic modulo irrelevant homology, which we call a free Cox complex for M. These complexes have many advantages over minimal free resolutions over smooth toric varieties other than projective spaces. We develop this in detail for products of projective spaces. This is joint work with Daniel Erman and Gregory G. Smith

Existence and Applications of Ricci Flows via Pseudolocality

Stephen Shipman: Fast Computation of 2D-Periodic Green Functions in 3D Near Cutoff Frequencies

##### Abstract:

We present an efficient method for computing wave scattering by 2D-periodic diffraction gratings in 3D space near cutoff frequencies, at which a Rayleigh wave is at grazing incidence to the grating. At these frequencies (a.k.a. Wood-anomaly frequencies), the spatial lattice sum for the quasi-periodic Green function diverges (the Green function doesn’t even exist!). We present a modification of this lattice sum by images, which results in algebraic convergence. Away from cutoff frequencies, one can actually obtain super-algebraic convergence to the unmodified quasi-periodic Green function by smooth truncation—however, realization of this convergence rate degenerates close to cutoff and one needs to invoke images. This is joint work with O. Bruno, C. Turc, and S. Venakides.

SIAM Student Chapter Reading Group Seminar

Mixed Boundary Value Problem in Unbounded Domains for Elliptic equations of Second Order

##### Abstract:

In this paper we will investigate regularity problem at infinity for solutions of elliptic equations of second order with respect to mixed Dirichlet and Neumann boundary conditions. We will show that under some assumption on Dirichlet and Neumann parts of the boundary, the solution is regular at in infinity.

First this type of test was obtained in a breakthrough work by Vladimir Mazya for elliptic equations in divergent form in "An analogue of Wiener's criterion for the Zaremba problem in a cylindrical domain." Funktsional. Anal. i Prilozhen. 16 (1982), No. 4.

In the current research both divergent and non-divergent equations will be considered. Main result for divergent equations is a part of a joint project with Alexander Grigoryan from Bielefield University. The main result for non-divergent equations is a joint project with Alexander Nazarov from St. Petersburg Department of V.A.Steklov Institute of Mathematics.

Algebraic Geometry

Sang-Hyun Oh: Tutorial on Plasmonics

Algebraic Geometry Reading Group Seminar

Differential Geometry and Symplectic Topology seminar

Amit Singer: PCA from Noisy Linearly Reduced Measurements

##### Abstract:

We consider the problem of estimating the covariance of X from measurements of the form y_i = A_i*x_i + e_i (for i = 1, . . . , n) where x_i are i.i.d. unobserved samples of X, A_i are given linear operators, and e_i represent noise. Our estimator is constructed efficiently via a simple linear inversion using conjugate gradient performed after eigenvalue shrinkage motivated by the spike model in high dimensional PCA. Applications to 2D image denoising, 3D ab-initio modelling, and 3D structure classification in single particle cryo-electron microscopy will be discussed.

Amit Singer is a Professor of Mathematics and member of the Executive Committee of the Program in Applied and Computational Mathematics (PACM) and of the Executive Committee for the Center for Statistics and Machine Learning (CSML) at Princeton University. He joined Princeton as an Assistant Professor in 2008. From 2005 to 2008 he was a Gibbs Assistant Professor in Applied Mathematics at the Department of Mathematics, Yale University. Singer received the BSc degree in Physics and Mathematics and the PhD degree in Applied Mathematics from Tel Aviv University (Israel), in 1997 and 2005, respectively. He served in the Israeli Defense Forces during 1997-2003. His list of awards includes a National Finalist for Blavatnik Awards for Young Scientists (2016), Moore Investigator in Data-Driven Discovery (2014), the Simons Investigator Award (2012), the Presidential Early Career Award for Scientists and Engineers (2010), the Alfred P. Sloan Research Fellowship (2010) and the Haim Nessyahu Prize for Best PhD in Mathematics in Israel (2007). His current research in applied mathematics focuses on theoretical and computational aspects of data science, and on developing computational methods for structural biology.

Climate Change Seminar

Amit Singer: PCA from Noisy Linearly Reduced Measurements

##### Abstract:

Amit Singer (Princeton University) We consider the problem of estimating the covariance of X from measurements of the form y_i = A_i*x_i + e_i (for i = 1, . . . , n) where x_i are i.i.d. unobserved samples of X, A_i are given linear operators, and e_i represent noise. Our estimator is constructed efficiently via a simple linear inversion using conjugate gradient performed after eigenvalue shrinkage motivated by the spike model in high dimensional PCA. Applications to 2D image denoising, 3D ab-initio modelling, and 3D structure classification in single particle cryo-electron microscopy will be discussed. Amit Singer is a Professor of Mathematics and member of the Executive Committee of the Program in Applied and Computational Mathematics (PACM) and of the Executive Committee for the Center for Statistics and Machine Learning (CSML) at Princeton University. He joined Princeton as an Assistant Professor in 2008. From 2005 to 2008 he was a Gibbs Assistant Professor in Applied Mathematics at the Department of Mathematics, Yale University. Singer received the BSc degree in Physics and Mathematics and the PhD degree in Applied Mathematics from Tel Aviv University (Israel), in 1997 and 2005, respectively. He served in the Israeli Defense Forces during 1997-2003. His list of awards includes a National Finalist for Blavatnik Awards for Young Scientists (2016), Moore Investigator in Data-Driven Discovery (2014), the Simons Investigator Award (2012), the Presidential Early Career Award for Scientists and Engineers (2010), the Alfred P. Sloan Research Fellowship (2010) and the Haim Nessyahu Prize for Best PhD in Mathematics in Israel (2007). His current research in applied mathematics focuses on theoretical and computational aspects of data science, and on developing computational methods for structural biology.

Approximating Functions with Singularities

##### Abstract:

Title: Approximating Functions with Singularities

Epstein zeta functions, III

Artin induction for ring spectra and algebraic K-theory

##### Abstract:

A theorem of Mitchell states that the chromatic complexity of the algebraic K-theory spectrum of a discrete ring R is bounded by one, i.e., the Morava K-theory vanishes at heights at least two. We give an approach for bounding the chromatic complexity in the algebraic K-theory of ring spectra.

Let R be a ring spectrum. We say that R-based Artin induction holds for a family of groups if for every finite group G, the rationalized Grothendieck group of the category of perfect R-modules with G-action is induced from the given family. We show that Artin induction theorems can be used to bound chromatic complexity and give several examples in ring spectra, in line with the redshift philosophy of Rognes. This is joint work with Dustin Clausen, Niko Naumann, and Justin Noel.

Student Number Theory Seminar

Reading Seminar for Automorphic Forms

Empirical Minimum Variance Delta hedging

##### Abstract:

This presentation will review the recent paper "Optimal Delta Hedging for Options" (Hull and White, 2016). The goal of Delta-hedging is to minimize the variance of a portfolio's value change as the underlying moves. The usual Black-Scholes Delta does not accomplish this goal, as it ignores the non-zero correlation between the movement of the underlying and the implied volatility. Hull and White propose a simple method of adjusting Delta based on historical data, producing better hedging results for options on the S&P500 index.

Bio: Dr. Javier Acosta got this PhD from the University of Minnesota's School of Mathematics. His research interests include probability and game theory. Dr. Acosta works in the Quant Finance field. He has industry experience in both banking and insurance hedging.

Evenness of Reduced Word Graphs

##### Abstract:

The reduced expressions for a given element w of a Coxeter group (W, S) can be regarded as the vertices of a directed graph R(w); its arcs correspond to the braid moves. Specifically, an arc goes from a reduced expression a to a reduced expression b when b is obtained from a by replacing a contiguous subword of the form stst... (for some distinct s, t ? S) by tsts... (where both subwords have length the order of st). We prove a strong bipartiteness-type result for this graph R(w): Not only does every cycle of R(w) have even length; actually, the arcs of R(w) can be colored (with colors corresponding to the type of braid moves used), and to every color c corresponds an "opposite" color c^op (corresponding to the reverses of the braid moves with color c), and for any color c, the number of arcs in any given cycle of R(w) having color in {c, c^op} is even. This is generalizes and improves on a 2014 result by Bergeron, Ceballos and Labbé. I will also discuss some conjectures generalizing it even

further.

Lie Theory Seminar

Applied and Computational Math Colloquium

The energy landscape of the Sherrington-Kirkpatrick model

##### Abstract:

The Sherrington-Kirkpatirck (SK) model is a mean-field spin glass introduced by theoretical physicists in order to explain the strange behavior of certain alloy, such as CuMn. Despite of its seemingly simple formulation, it was conjectured to possess a number of fruitful properties. This talk will be focused on the energy landscape of the SK model. First, we will present a formula for the maximal energy in Parisi's formulation. Second, we will give a description of the energy landscape by showing that near any given energy level between zero and maximal energy, there exist exponentially many equidistant spin configurations. Based on joint works with Auffinger, Handschy, and Lerman.

SIAM Internship Panel

##### Abstract:

The event will have graduate students speaking about their experiences with their summer internships and professors speaking about their experience facilitating internships. Following their talks, we will have a question and answer session. Food and beverages will be provided at the event. The participants of the Graduate Student Internship Panel will be: Prof. Gilad Lerman, Paula Dasbach (interned at Medtronic), Tyler Maunu (NGA), Swayambhoo Jain (interned at Yahoo), Hailee Peck (interned at Los Alamos). The event is organized by the SIAM Student Chapter at the University of Minnesota.

Student Combinatorics Seminar

Colloquium - TBA

Algebraic Geometry Reading Group Seminar

Properties of Translating Solitons

##### Abstract:

We discuss various properties of translating soliton hypersurfaces in R^{n+1}. We also consider their monotonicity formula, Kato inequality, and some Bernstein type results. The main material is from a joint work M. Vicente.

SIAM Student Chapter Reading Group Seminar

Math Club

The Sandpile Group of a Finite Group Representation

##### Abstract:

(joint work with G. Benkart and C. Klivans; arXiv:1601.06849)

For any (finite-dimensional, faithful, complex) representation of a finite group G,

we define a new invariant, which one might call its "sandpile group". This invariant is a finite abelian group, but also has a natural commutative product: it is the augmentation ideal for a certain quotient of the commutative ring of virtual characters of G. It also bears a close relation to the McKay correspondence.

The goal in this talk will be to define this invariant, compute a few examples, and advertise an example where it is an open combinatorial challenge to compute its structure completely. It is our hope that more commutative algebraic technique might help in resolving this.

Geometric Analysis Learning Seminar

C. Eugene Wayne: The Derivation and Justification of Modulation Equations for Optical Systems

##### Abstract:

“Modulation” or “Amplitude” equations are simplified equations that are believed to capture the essentials of the behavior of more complicated physical systems. Examples include the Korteweg-de Vries equation (KdV), the nonlinear Schroedinger equation (NLS) and Ginzburg-Landau equation. They arise in many different physical contexts and serve as prototypical examples or “normal forms” for a variety of nonlinear phenomena. This talk will focus on the derivation of the NLS equation as an approximation to describe the propagation of pulses in nonlinear optical fibers and will also discuss how one can derive rigorous estimates for the difference between the approximation given by the NLS equation and the true solution of the more complicated physical system. If time permits I will also discuss possible modulation equations for regimes in which the NLS approximation breaks down.

SIAM Student Chapter Reading Group Seminar

Poisson stochastic Process and Basic Schauder and Sobolev-Space Estimates in the Theory of Parabolic Equations

##### Abstract:

We show how knowing Schauder and Sobolev-space estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs for equations with coefficients depending only on time variable with the SAME constants as in the case of the one-dimensional heat equation. The method is based on using the Poisson stochastic process. It looks like no other method is available at this time and it is a very challenging problem to find a purely analytic approach to proving such results. Joint work with E. Priola.

New Relations on Caporaso-Harris Invariants and More

##### Abstract:

Caporaso-Harris invariants count the number of nodal curves on theprojective plane satisfying given tangency conditions with a line. Those invariants are first proved to satisfy a recursive formula in1996 and then showed to be polynomials in the degree (when the degreeis large enough) using tropical geometry in 2009. On the other hand, the number of nodal curves are already known to be universal polynomials of the Chern numbers for any surfaces and line bundles. Inthis talk we will discuss a new type of relations for Caporaso-Harrisinvariants which unify these features and in fact also hold on all smooth varieties.

Algebraic Geometry Reading Group Seminar

Differential Geometry and Symplectic Topology seminar

Xiuyuan Cheng: Limiting Spectrum of Random Kernel Matrices

##### Abstract:

We consider n-by-n matrices whose (i, j)-th entry is f(X_i^T X_j), where X_1, ...,X_n are i.i.d. standard Gaussian random vectors in R^p, and f is a real-valued function. The eigenvalue distribution of these kernel random matrices is studied in the "large p, large n" regime. It is shown that with suitable normalization the spectral density converges weakly, and we identify the limit. Our analysis applies as long as the rescaled kernel function is generic, and particularly, this includes non-smooth functions, e.g. Heaviside step function. The limiting densities "interpolate" between the Marcenko-Pastur density and the semi-circle density.

Xiuyuan Cheng is currently a Gibbs Assistant Professor at the Program of Applied Mathematics of Yale University. Before joining Yale, she was a Postdoctoral Researcher in Département d'Informatique of École normale supérieure, France, from 2013 to 2015. She received her Ph.D. from the Program of Applied and Computational Mathematics at Princeton University in 2013, advised jointly by Prof. Amit Singer and Prof. Weinan E. Her research focuses on high dimensional data analysis and mathematical theories of machine learning.

Climate Change Seminar

##### Abstract:

An Introduction to Budyko's Equation

Epstein zeta functions, II

Approximating Functions with Singularities

##### Abstract:

Title: Approximating Functions with Singularities

Topology Seminar

Student Number Theory Seminar

##### Abstract:

Title: A Crash Course in Lie Theory and Reductive Groups

Abstract: Reductive groups such as GL(n), O(n), and Sp(n) are ubiquitous in modern mathematics. The structure theory of such groups (over a smorgasbord of fields) is well understood yet quite verbose, which can make a large swath of mathematics impenetrable to the uninitiated. I will introduce some of the "major players" in the study of reductive groups, emphasizing examples and intuition to help orient a newcomer to the field. In particular, I hope to

explain what a reductive group is

discuss the Lie algebra of a reductive group

introduce important subgroups (or subalgebras) of these groups (or Lie algebras), and

state/allude to the finite type classification of semisimple Lie algebras.

This talk is geared towards first and second year graduate students who have not yet taken Lie Groups and Lie Algebras.

Reading Seminar for Automorphic Forms

MFM Alumni/Current Student Panel

##### Abstract:

A variety of local quantitive analysts, investment analysts who are alumni of the MFM and 2nd year MFM students will talk to the incoming MFM class and other interested students and individuals about: (1) what they learned in the MFM, (2) what helped them find internships and jobs and (3) the most important things to do to take advantage of all during your time in the program: academics, program activiites as well as related opportunities in town and across the country/globe to learn more about the field of Quantitative Finance

The Greedy Basis Equals the Theta Basis: A Rank Two Haiku

##### Abstract:

In groundbreaking work from a few years ago, K. Lee, L. Li, and A. Zelevinsky constructed a basis for any rank 2 cluster algebra that consists of a special family of indecomposable positive elements. They coined the term Greedy Basis for this construction and illustrated a combinatorial interpretation of the Laurent expansions of its elements using Dyck paths. Ensuing work by M. Gross, P. Hacking, S. Keel, and M. Kontsevich used algebraic geometry, as inspired by mirror symmetry and tropical geometry, to define the Theta Basis for any cluster algebra. The construction of the theta basis can be described in terms of the machinery of broken lines and scattering diagrams.

In this talk, these two bases will be constructed, assuming no prior knowledge, and compared. In particular, I will discuss joint work with M. Cheung, M. Gross, G. Muller, D. Rupel, S. Stella, and H. Williams started at an AMS Mathematical Research Community, in which we equate these two bases in the rank two case. This talk will be accessible for graduate students and advanced undergraduates.

Lie Theory Seminar

Unraveling Kidney Physiology, Pathophysiology and Therapeutics: A Modeling Approach

##### Abstract:

The kidney not only filters metabolic wastes and toxins from the body,but it also regulates the body's water balance, electrolyte balance, and acid-base balance, blood pressure, and blood flow. Despite intense research, aspects of kidney functions remain incompletely understood. I will discuss how our group use mathematical modeling techniques to address a host of previously unanswered questions in renal physiology and pathophysiology: Why is the mammalian kidney so susceptible to hypoxia, despite receiving ~25% of the cardiac output? What are the mechanisms underlying the development of acute kidney injury in a patient who has undergone cardiac surgery performed on cardiopulmonary bypass? What is the effect of inhibiting sodium-glucose transport, a novel treatment for reducing renal glucose update in diabetes, on renal NaCl transport and oxygen consumption?

Algebraically inspired results on convex functions

##### Abstract:

In this talk we will discuss new identities and constructions involving convex functions. These results demonstrate surprising formal similarities between the Legendre transform and the inversion map (say on positive real numbers). In this sense, these results are "algebraically motivated". As corollaries we will discuss decompositions of the Gaussian function, as well as a Blaschke-Santaló type result involving the Gaussian measure.

Student Combinatorics Seminar

Colloquium - TBA

Algebraic Geometry Reading Group Seminar

SIAM Student Chapter Reading Group Seminar

Differential Geometry and Symplectic Topology seminar

Math Club

Multiplicative structures on minimal free resolutions of monomial ideals

##### Abstract:

The minimal free resolution of a quotient of the polynomial ring admits a (generally non-associative) multiplication which satisfies the Leibniz rule. This multiplication is far from being unique and in favorable cases it can be chosen to be associative, which makes the resolution into a DGA. In this talk, I consider these multiplicative structures in the setting of monomial ideals. On the one hand, I will present some structure theorems about these multiplications, in particular in the associative case. On the other hand, I will show that the presence of an associative multiplication has implications on the possible Betti numbers of the ideal.

Geometric Analysis Learning Seminar

SIAM Student Chapter Reading Group Seminar

PDE Seminar - Spreading fronts in the anisotropic Allen-Cahn equations on R^n

##### Abstract:

We consider the Cauchy problem for the anisotropic Allen-Cahn equation on R^n with n\geq 2, and analyze the large time behavior of the solutions with spreading fronts. Our result states that, under some mild assumptions on

the initial value, the solution develops a well-formed front whose position roughly coincides with the spreading Wulff shape. This is a joint work with Hiroshi Matano in University of Tokyo and Yoichiro Mori in University of Minnesota.

Algebraic Geometry Seminar

Differential Geometry and Symplectic Topology seminar

Climate Change Seminar

##### Abstract:

An Introduction to Energy Balance

Epstein zeta functions and their zeros

Approximating Functions with Singularities

##### Abstract:

Title: Approximating Functions with Singularities

Topology Seminar

Student Number Theory Seminar

Reading Seminar for Automorphic Forms

Matrix Ball construction for affine Robinson-Schensted correspondence

##### Abstract:

In his study of Kazhdan-Lusztig cells in affine type A, Shi

has introduced an affine analog of Robinson-Schensted correspondence.

We generalize the Matrix-Ball Construction of Viennot and Fulton to

give a more combinatorial realization of Shi's algorithm. As a

byproduct, we also give a way to realize the affine correspondence via

the usual Robinson-Schensted bumping algorithm. Next, inspired by

Honeywill, we extend the algorithm to a bijection between the extended

affine symmetric group and collection of triples (P,Q,r) where

P and Q are tabloids and r is a dominant weight.

Boaz Nadler: Unsupervised Ensemble Learning

##### Abstract:

In various applications, one is given the advice or predictions of several classifiers of unknown reliability, over multiple questions or queries. This scenario is different from standard supervised learning where classifier accuracy can be assessed from available labeled training or validation data, and raises several questions: Given only the predictions of several classifiers of unknown accuracies, over a large set of unlabeled test data, is it possible to

a) reliably rank them, and

b) construct a meta-classifier more accurate than any individual classifier in the ensemble?

In this talk we'll show that under various independence assumptions between

classifier errors, this high dimensional data hides simple low dimensional

structures. Exploiting these, we will present simple spectral methods to address

the above questions, and derive new unsupervised spectral meta-learners.

We'll prove these methods are asymptotically consistent when

the model assumptions hold, and present their empirical success on a variety

of unsupervised learning problems.

Unsupervised Ensemble Learning

##### Abstract:

Speaker:Boaz Nadler / Weizmann Institute of Science, Israel

Abstract:

In various applications, one is given the advice or predictions of several classifiers of unknown reliability, over multiple questions or queries. This scenario is different from standard supervised learning where classifier accuracy can be assessed from available labeled training or validation data,

and raises several questions. Given only the predictions of several classifiers of unknown accuracies, over a large set of unlabeled test data, is it possible to:

a) reliably rank them, and

b) construct a meta-classifier more accurate than any

individual classifier in the ensemble?

In this talk we'll show that under various independence assumptions between classifier errors, this high dimensional data hides simple low dimensional structures. Exploiting these, we will present simple spectral methods to address the above questions, and derive new unsupervised spectral meta-learners.

We'll prove these methods are asymptotically consistent when

the model assumptions hold, and present their empirical success on a variety of unsupervised learning problems.

Parabolic Harnack inequalities and Poincare inequalities on Dirichlet spaces

##### Abstract:

This talk will discuss old and new results on parabolic Harnack inequalities and Poincare inequalities on metric measure Dirichlet spaces with a doubling measure. For the case of Riemannian manifolds, it is known from the works of Grigor'yan and Saloff-Coste that the Harnack inequality is equivalent to two-sided Gaussian heat kernel estimates, as well as to the Poincare inequality together with the volume doubling property. Subsequent work by Sturm has then opened the door to related equivalence results on Dirichlet spaces. The focus of this talk will be on the case of non-symmetric operators, fractal-type spaces, as well as on relaxing the requirement that the metric be geodesic. Time permitting, I may also present estimates for non-symmetric heat kernels on fractal spaces.