# Past Seminars

Fri Apr 16

## MCFAM Seminar

12:00pm - Zoom: https://umn.zoom.us/j/94564033758
Efficient Exposure Frontiers

##### Abstract:

Abstract: Risk is described by the instantaneous exposure to changes in valuations induced by the arrival rate of economic shocks. The arrival rate mea- sure is typically not a probability measure and often the aggregate arrival rate across all shocks is infinite. Risk management and portfolio theory are conse- quently recast as managing this exposure risk. There is no risk free exposure with all fixed income securities subject to the risks of instantaneous changes in their valuations. The reference return in the economy is that of a zero risk gra- dient return, typically estimated as negative. Required returns on assets with low risk gradients are then negative. It is also observed that required returns are robust to positions on the efficient frontier as well the construction of the frontier itself. Both equity and fixed income security frontiers are constructed as illustrations of efficient risk positions.

BIO: Dilip Madan is Professor of Finance at the Robert H. Smith School of Business. He specializes in Mathematical Finance. Currently he serves as a consultant to Morgan Stanley, Meru Capital and Caspian Capital. He has also consulted with Citigroup, Bloomberg, the FDIC and Wachovia Securities. He is a founding member and Past President of the Bachelier Finance Society. He received the 2006 von Humboldt award in applied mathematics, was the 2007 Risk Magazine Quant of the year, received the 2008 Medal for Science from the University of Bologna and held the 2010 Eurandom Chair. He is Managing Editor of Mathematical Finance, Co-editor of the Review of Derivatives Research, Associate Editor of the Journal of Credit Risk and Quantitative Finance. His work is dedicated to improving the quality of financial valuation models, enhancing the performance of investment strategies, and advancing the efficiency of risk allocation in modern economies. Recent major contributions have appeared inMathematical Finance, Finance and Stochastics, Quantitative Finance, the Journal of Computational Finance, The International Journal of Theoretical and Applied Finance, The Journal of Risk, The Journal of Credit Risk among other journals.

Thu Apr 15

## Colloquium

3:30pm - Zoom ID 91514486597 (contact faculty for pw)
Large deviations for lacunary trigonometric sums
Kavita Ramanan, Brown University
##### Abstract:

Lacunary trigonometric sums are known to exhibit several properties that are typical of sums of iid random variables such as the central limit theorem, established by Salem and Zygmund, and the law of the iterated logarithm, due to Erdos and Gal. We study large deviation principles for such sums, and show that they display several interesting features, including sensitivity to the arithmetic properties of the corresponding lacunary sequence. This is joint work with C. Aistleitner, N. Gantert, Z. Kabluchko and J. Prochno.

Thu Apr 15

11:15am - Zoom
Climate Seminar
TBA
Wed Apr 14

## Probability Seminar

9:00am - via Zoom
Multiple Equilibria and Resilience in Large Complex Systems: beyond May-Wigner model
Yan Fyodorov, King's College London
##### Abstract:

I will discuss two different models of randomly coupled N>>1 autonomous differential equations with the aim of counting their fixed points (aka equilibria), and classifying them by their ''instability index'', i.e. the number of unstable directions. In the first model ( studied in a joint paper with G. Ben Arous & B. Khoruzhenko) characterized by both translational and rotational statistical symmetry of the vector field, we estimate the probability of an equilibrium to have a given index in a phase with exponentially many equilibria. In the second model (studied with S. Belga Fedeli & J. Ipsen) characterized by only rotational statistical symmetry around a chosen stable equilibrium, we find a characteristic distance beyond which the multitude of equilibria prevents a trajectory to go towards the stable equilibrium. This may help to shed some light on ''resilience'' mechanisms of complex ecosystems.

Tue Apr 13

## IMA Data Science Lab Seminar

1:25pm - Zoom
Quantile-based Iterative Methods for Corrupted Systems of Linear Equations
Elizaveta Rebrova, University of California, Los Angeles
##### Abstract:

One of the most ubiquitous problems arising across the sciences is that of solving large-scale systems of linear equations Ax = b. When it is infeasible to solve the system directly by inversion, light and scalable iterative methods can be used instead, such as, Randomized Kaczmarz (RK) algorithm, or Stochastic Gradient Descent (SGD). The classical extensions of RK/SGD to noisy (inconsistent) systems work by showing that the iterations of the method still approach the least squares solution of the system until a certain convergence horizon (that depends on the noise size). However, in order to handle large, sparse, potentially adversarial corruptions, one needs to modify the algorithms to avoid corruptions rather than try to tolerate them -- and quantiles of the residual provide a natural way to do so. In this talk, I present QuantileRK and QuantileSGD, the versions of two classical iterative algorithms aimed at linear systems with adversarially corrupted vector b. Our methods work on up to 50% of incoherent corruptions, and up to 20% of adversarial corruptions (that consistently create an "alternative" solution of the system). Our theoretical analysis shows that under some standard assumptions on the measurement model, despite corruptions of any size, both methods converge to the true solution with exactly the same rate as RK on an uncorrupted system up to an absolute constant. Based on the joint work with Jamie Haddock, Deanna Needell, and Will Swartworth.

Liza Rebrova is currently a postdoctoral scholar at the Computational Research Division of the Lawrence Berkeley National Lab. From 2018 to the end of 2020, she worked as an Assistant Adjunct Professor at the UCLA Department of Mathematics (Computational and Applied Math Group, mentored by Professors Deanna Needell and Terence Tao). She received a Ph.D. in Mathematics from the University of Michigan in 2018 (advised by Prof. Roman Vershynin) and a Specialist degree from Moscow State University in 2012. Her research involves interactions with high-dimensional probability, random matrix theory, mathematical data science, and numerical linear algebra, with the main goal to study large high-dimensional data objects in the presence of randomness and to develop randomized algorithms that efficiently process complex data. She is a recipient of the Allen Shields Memorial Fellowship (UofMichigan, 2018) and postdoctoral sponsorship by Capital Fund Management (UCLA, 2018-2020).

Tue Apr 13

## Dynamical Systems

12:20pm - See abstract for Zoom info
Multivariate Climate Projections: More Accurate Equilibrium Estimations & Evolution of Climate Feedbacks
Robbin Bastiaansen, Utrecht University
##### Abstract:

When the climate system is forced by e.g. changes in atmospheric CO2, it responds to this change on multiple time scales, showing responses on time scales ranging from very short to very long. It is clear that the behavior over these time scales can be very different: for instance, as ice melts, the ice-albedo feedback becomes less and less important. Predominantly used climate projection methods, however, typically do not adequately take such state changes into account and are univariate: they only consider the global mean surface temperature -- assuming everything else is just linearly correlated to that. In this talk, I will show multivariate estimation techniques that are capable of tracking these state changes by incorporating additional observables into the analysis directly. This has two important advantages. First, such methods are better equipped to provide projections for the longer time scales (for instance, estimations of equilibrium climate sensitivity). Second, it makes it possible to estimate other observables directly -- without making assumptions on their relation to the global mean surface temperature -- which leads to better quantitative insights in how precisely the climate will change in the future (for instance, how climate feedback processes might change over time).Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Apr 13

11:15am - Zoom
Climate Seminar
TBA
Mon Apr 12

## Applied and Computational Mathematics Seminar

3:35pm - via Zoom
Graph-based Bayesian semi-supervised learning: prior design and posterior contraction.
Daniel Sanz-Alonso, University of Chicago
##### Abstract:

In this talk I will introduce graphical representations of stochastic partial differential equations that allow to approximate Matern Gaussian fields on manifolds and generalize the Matern model to abstract point clouds. Under a manifold assumption, approximation error guarantees will be established building on the theory of spectral convergence of graph Laplacians. Graph-based Matern prior models facilitate computationally efficient inference and sampling exploiting sparsity of the precision matrix. Moreover, we will show that they are natural priors for Bayesian semi-supervised learning and can give optimal posterior contraction. This is joint work with Ruiyi Yang.

Mon Apr 12

## Topology Seminar

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

Mon Apr 12

## Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Apr 12

## Special Events and Seminars

11:00am - via Zoom https://umn.zoom.us/j/97639815760
HA-GMT-PDE Seminar
##### Abstract:

Titles and abstracts of the talks will be made available close to each talk at the seminar website https://sites.google.com/view/hagmtpdeseminar. To subscribe to the weekly seminar mailing list, please contact Bruno Poggi Cevallos, at poggi008@umn.edu. The seminar is organized by Bruno Poggi Cevallos (University of Minnesota), Ryan Matzke (University of Minnesota), and José Luis Luna García (University of Missouri).

Thu Apr 08

11:15am - Zoom
Climate Seminar
TBA
Wed Apr 07

## Probability Seminar

9:00am - via Zoom
Branching random walks, characteristic polynomials, and zeta: log-correlation, moments, and extrema
Emma Bailey, University of Bristol
##### Abstract:

In this talk I will introduce three log-correlated processes and present results on their moments (and moments of moments), and how these relate to their extremes.  This study features connections with integrable systems (in particular Toeplitz and Hankel determinants), RH problems, the Fyodorov-Hiary-Keating conjectures, Painlev\'e equations, Young diagrams and Gelfand-Tsetlin patterns, large deviations and more.

This talk will include work joint with Louis-Pierre Arguin, Theo Assiotis, Jon Keating.

Tue Apr 06

## Commutative Algebra Seminar

3:35pm - via Zoom
Commutative Algebra Seminar

Tue Apr 06

## IMA Data Science Lab Seminar

1:25pm - Zoom
The Ramanujan Machine: Using Algorithms for the Discovery of Conjectures on Mathematical Constants
Ido Kaminer, Technion-Israel Institute of Technology
##### Abstract:

In the past, new conjectures about fundamental constants were discovered sporadically by famous mathematicians such as Newton, Euler, Gauss, and Ramanujan. The talk will present a different approach – a systematic algorithmic approach that discovers new mathematical conjectures on fundamental constants. We call this approach “the Ramanujan Machine”. The algorithms found dozens of well-known formulas as well as previously unknown ones, such as continued fraction representations of π, e, Catalan’s constant, and values of the Riemann zeta function. Part of the conjectures were in retrospect simple to prove, whereas others remained so far unproved. We will discuss these puzzles and wider open questions that arose from this algorithmic investigation – specifically, a newly-discovered algebraic structure that seems to generalize all the known formulas and connect between fundamental constants. We will also discuss two algorithms that proved useful in finding conjectures: a variant of the meet-in-the-middle algorithm and a gradient descent algorithm tailored to the recurrent structure of continued fractions. Both algorithms are based on matching numerical values; consequently, they conjecture formulas without providing proofs or requiring prior knowledge of the underlying mathematical structure. This way, our approach reverses the conventional usage of sequential logic in formal proofs; instead, using numerical data to unveil mathematical structures and provide leads to further mathematical research.
Ido Kaminer joined the Technion as an assistant professor and an Azrieli Faculty Fellow in 2018, after a postdoc at MIT as a Rothschild Fellow, MIT-Technion Fellow, and a Marie Curie Fellow. In his PhD, Ido discovered new classes of accelerating beams in nonlinear optics and electromagnetism, for which he received the 2012 Israel Physical Society Prize, and the 2014 APS (American Physical Society) Award for Outstanding Doctoral Dissertation in Laser Science. Ido was the first Israeli to ever win an APS award for his PhD thesis. He was chosen to the 2020 list of 40 promising leaders under 40 by TheMarker and won multiple awards and grants recently including the ERC Starting Grant, and the 2021 Blavatnik Award for Young Scientists in Israel.

Tue Apr 06

11:15am - Zoom
Climate Seminar
TBA
Mon Apr 05

## Topology Seminar

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

Mon Apr 05

## Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Apr 05

## Special Events and Seminars

11:00am - via Zoom https://umn.zoom.us/j/95075343173
HA-GMT-PDE Seminar
Mariana Smit Vega Garcia&nbsp;, Western Washington University
##### Abstract:

Titles and abstracts of the talks will be made available close to each talk at the seminar website https://sites.google.com/view/hagmtpdeseminar. To subscribe to the weekly seminar mailing list, please contact Bruno Poggi Cevallos, at poggi008@umn.edu. The seminar is organized by Bruno Poggi Cevallos (University of Minnesota), Ryan Matzke (University of Minnesota), and José Luis Luna García (University of Missouri).

Thu Apr 01

## Colloquium

3:30pm - Via Zoom ID 91514486597 (contact faculty for pw)
Electric-magnetic duality between periods and L-functions
David Ben-Zvi, University of Texas, Austin
##### Abstract:

I will describe joint work with Yiannis Sakellaridis and Akshay Venkatesh, in which ideas originating in quantum field theory are applied to a problem in number theory.

A fundamental tool in number theory, the relative Langlands program, is centered on the representation of L-functions of Galois representations as integrals of automorphic forms. However, the data that naturally index these period integrals (spherical varieties for a reductive group G) and the L-functions (representations of the Langlands dual group G^) don't seem to line up, making the search for integral representations somewhat of an art.

We present an approach to this problem via the Kapustin-Witten interpretation of the [geometric] Langlands correspondence as electric-magnetic duality for 4-dimensional supersymmetric gauge theory. Namely, we rewrite the *relative* Langlands program as duality in the presence of boundary conditions. As a result the partial correspondence between periods and L-functions is embedded in a natural duality between Hamiltonian actions of the dual groups.

Thu Apr 01

11:15am - Zoom
Climate Seminar
TBA
Wed Mar 31

## Probability Seminar

4:00pm - via Zoom
Extremal and critical eigenvalue statistics of random matrices
Benjamin Landon, MIT
##### Abstract:

We discuss recent results on classes of random eigenvalue statistics of critical or extremal nature. The study of the largest gap between consecutive eigenvalues of random matrices was first urged by Diaconis with the goal of understanding the correspondence between random matrices and number theory. We present a comparison theorem that shows that this quantity is universal within the class of generalized Wigner matrices. The fluctuations of a single bulk eigenvalue and the eigenvalue counting function were determined by Gustavsson for the GUE. We discuss the universality of these quantities for general classes of matrices, and lower order corrections showing that these quantities are essentially on the boundary between universal and non-universal fluctuations.

Joint work with P. Lopatto, J. Marcinek and P. Sosoe

Wed Mar 31

## PDE Seminar

3:35pm - Zoom
A capillarity model for soap films
Darren King, UT Austin
##### Abstract:

We study a variational model for soap films based on capillarity theory and its relation to minimal surfaces. Here, soap films are modelled, not as surfaces, but as regions of small volume satisfying a homotopic spanning condition.Join Zoom Meetinghttps://umn.zoom.us/j/91765959125?pwd=RjRkSW9PNi9HNzVOb2lwb0tkWVVoZz09Meeting ID: 917 6595 9125Passcode: VinH16

Tue Mar 30

## IMA Data Science Lab Seminar

1:25pm - Zoom
Deep Networks and the Multiple Manifold Problem
John Wright, Columbia University
##### Abstract:

Data with low-dimensional nonlinear structure are ubiquitous in engineering and scientific problems. We study a model problem with such structure—a binary classification task that uses a deep fully-connected neural network to classify data drawn from two disjoint smooth curves on the unit sphere. Aside from mild regularity conditions, we place no restrictions on the configuration of the curves. We prove that when (i) the network depth is large relative to certain geometric properties that set the difficulty of the problem and (ii) the network width and number of samples is polynomial in the depth, randomly-initialized gradient descent quickly learns to correctly classify all points on the two curves with high probability. To our knowledge, this is the first generalization guarantee for deep networks with nonlinear data that depends only on intrinsic data properties. Our analysis draws on ideas from harmonic analysis and martingale concentration for handling statistical dependencies in the initial (random) network. We sketch applications to invariant vision, and to gravitational wave astronomy, where leveraging low-dimensional structure leads to statistically optimal tests for identifying signals in noise.

Joint work with Sam Buchanan, Dar Gilboa, Tim Wang, Jingkai Yan

John Wright is an associate professor in Electrical Engineering at Columbia University. He is also affiliated with the Department of Applied Physics and Applied Mathematics and Columbia’s Data Science Institute. He received his PhD in Electrical Engineering from the University of Illinois at Urbana Champaign in 2009. Before joining Columbia he was with Microsoft Research Asia from 2009-2011. His research interests include sparse and low-dimensional models for high-dimensional data, optimization (convex and otherwise), and applications in imaging and vision. His work has received a number of awards and honors, including the 2012 COLT Best Paper Award and the 2015 PAMI TC Young Researcher Award.

Tue Mar 30

## Dynamical Systems

12:20pm - See abstract for Zoom info
Topological Data Analysis for Dynamic Data in Intracellular Transport
Veronica Ciocanel, Duke University
##### Abstract:

Actin filaments are polymers that interact with motor proteins inside cells and play important roles in cell motility, shape, and development. Depending on its function, this dynamic network of proteins reshapes and organizes in a variety of structures, including bundles, clusters, and contractile rings. Motivated by observations from the roundworm, we use an agent-based modeling framework to study interactions between filaments and motor proteins inside cells. We develop a method based on topological data analysis to understand time-series data extracted from these dynamical systems models of filament interactions. We use this technique to compare the filament organization resulting from motors with different properties. This approach also raises research questions about how to assess the significance of topological features in common topological summary visualizations, especially for data from dynamic simulations.

Tue Mar 30

11:15am - Zoom
Climate Seminar
TBA
Mon Mar 29

## Applied and Computational Mathematics Seminar

3:35pm - via Zoom
Applied and Computational Math

##### Abstract:

Speaker: Yulong Lu
Affiliation : University of Massachusetts, Amherst
Abstract: TBD

Mon Mar 29

## Applied and Computational Mathematics Seminar

3:35pm - via Zoom
Theoretical guarantees of machine learning methods for statistical sampling and PDEs in high dimensions
Yulong Lu, University of Massachusetts, Amherst
##### Abstract:

Neural network-based machine learning methods, including the most
notably deep learning have achieved extraordinary successes in
numerous fields. In spite of the rapid development of learning
algorithms based on neural networks, their mathematical analysis are far
from understood. In particular, it has been a big mystery that neural
network-based machine learning methods work extremely well for solving
high dimensional problems.

In this talk, I will demonstrate the power of neural network methods
for solving two classes of high dimensional problems: statistical
sampling and PDEs. In the first part of the talk, I will present a
universal approximation theorem of deep neural networks for representing
high dimensional probability distributions. In the second part of the
talk, I will discuss the generalization error analysis of the Deep Ritz
Method for solving high dimensional elliptic PDEs. For both
problems, our theoretical results show that neural networks-based
methods can overcome the curse of dimensionality.

Mon Mar 29

## Topology Seminar

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

Mon Mar 29

## Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Mar 29

## Special Events and Seminars

11:00am - via Zoom https://umn.zoom.us/j/98166893010
HA-GMT-PDE Seminar
Robin Neumayer, Northwestern University
##### Abstract:

Titles and abstracts of the talks will be made available close to each talk at the seminar website https://sites.google.com/view/hagmtpdeseminar. To subscribe to the weekly seminar mailing list, please contact Bruno Poggi Cevallos, at poggi008@umn.edu. The seminar is organized by Bruno Poggi Cevallos (University of Minnesota), Ryan Matzke (University of Minnesota), and José Luis Luna García (University of Missouri).

Fri Mar 26

## IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
Law - Math = Injustice: A Story of Conflict
Eric Ben-Artzi, Gannuity
##### Abstract:

This talk is about the conflicts of interest within the law enforcement bodies of our institutions, and the devastating consequences for organizations and society in general. It will look at the structural flaws in the gatekeeping apparatus from an abstract perspective, and at specific examples, especially from the speaker’s personal experience as a whistleblower at Deutsche Bank in the aftermath of the financial crisis. The important role for people with mathematical training will be highlighted.
Eric Ben-Artzi holds a PhD in mathematics from NYU, and is an expert in quantitative financial risk and valuation models. He worked for major Wall Street firms such as Goldman Sachs as well as small fin-tech startups such as BondIT. As a risk analyst at Deutsche Bank, he exposed a massive and complex accounting fraud. When internal reporting failed, Eric worked with an NGO and journalists to expose the conflicts of interest both within the bank and at law enforcement bodies. Eric teaches financial engineering courses at the Technion - Israel Institute of Technology, and is an advocate for legal reform.

Fri Mar 26

## MCFAM Seminar

12:00pm - Zoom: https://umn.zoom.us/j/94564033758
Do Jumps Matter in the Long Term? A Tale of Two Horizons
Jean-François Bégin, Simon Fraser University
##### Abstract:

Economic scenario generators (ESGs) for equities are important components of the valuation and risk management process of life insurance and pension plans. Because the resulting liabilities are very long-lived and the short-term performance of the assets backing these liabilities may trigger important losses, it is thus a desired feature of an ESG to replicate equity returns over such horizons. In light of this horizon duality, we investigate the relevance of jumps in ESGs to replicate dynamics over different horizons and compare their performance to popular models in actuarial science. We show that jump-diffusion models cannot replicate higher moments if estimated with the maximum likelihood. Using a generalized method of moments-based approach, however, we find that simple jump-diffusion models have an excellent fit overall (moments and the entire distribution) at different time scales. We also investigate three typical applications: the value of one dollar accumulated with no intermediate monitoring, a solvency analysis with frequent monitoring, and a dynamic portfolio problem. We find that jumps have long-lasting effects that are difficult to replicate otherwise, so yes, jumps do matter in the long term.

This is joint work with Mathieu Boudreault.

Bio: Jean-François Bégin, PhD, FSA, FCIA is an Assistant Professor in the Department of Statistics and Actuarial Science at Simon Fraser University. His research interests include financial modelling, financial econometrics, filtering methods, high-frequency data, credit risk, option pricing, and pension economics. Before joining SFU, he received his PhD from HEC Montréal.

Thu Mar 25

11:15am - Zoom
Climate Seminar
TBA
Thu Mar 25

## Colloquium

10:00am - Zoom ID 91514486597 (contact faculty for pw)
From differential equations to deep learning for image analysis
Carola-Bibiane Schönlieb, University of Cambridge
##### Abstract:

Images are a rich source of beautiful mathematical formalism and analysis. Associated mathematical problems arise in functional and non-smooth analysis, the theory and numerical analysis of partial differential equations, harmonic, stochastic and statistical analysis, and optimisation. Starting with a discussion on the intrinsic structure of images and their mathematical representation, in this talk we will learn about some of these mathematical problems, about variational models for image analysis and their connection to partial differential equations and deep learning. The talk is furnished with applications to art restoration, forest conservation and cancer research.

Wed Mar 24

## Probability Seminar

4:00pm - via Zoom
Probability Seminar
TBD
Tue Mar 23

## Commutative Algebra Seminar

3:35pm - via Zoom
Commutative Algebra Seminar

Tue Mar 23

## IMA Data Science Lab Seminar

1:25pm - Zoom
Jeffrey Rosenthal, University of Toronto
##### Abstract:

The Metropolis Algorithm is an extremely useful and popular method of approximately sampling from complicated probability distributions. "Adaptive" versions automatically modify the algorithm while it runs, to improve its performance on the fly, but at the risk of destroying the Markov chain properties necessary for the algorithm to be valid.  In this talk, we will illustrate the Metropolis algorithm using a very simple JavaScript example (http://probability.ca/jeff/js/metropolis.html).  We will then discuss adaptive MCMC, and present examples and theorems concerning its ergodicity and efficiency.
Jeffrey S. Rosenthal is a professor of Statistics at the University of Toronto, specializing in Markov chain Monte Carlo (MCMC) algorithms. He received his BSc from the University of Toronto at age 20, and his PhD in Mathematics from Harvard University at age 24. He was awarded the 2006 CRM-SSC Prize, the 2007 COPSS Presidents' Award, the 2013 SSC Gold Medal, and fellowship of the Institute of athematical Statistics and of the Royal Society of Canada. He has published well over one hundred research papers, and five books (including the Canadian bestseller Struck by Lightning: The Curious World of Probabilities). His web site is www.probability.ca, and on Twitter he is @ProbabilityProf.

Tue Mar 23

## Dynamical Systems

12:20pm - via Zoom
The Continuation of Conley's Attractor-Repeller Pair Decomposition for Differential Inclusions
Cameron Thieme, University of Minnesota&nbsp;
##### Abstract:

Over the past few decades, piecewise-continuous differential equations have become increasingly popular in scientific models.  In particular, conceptual climate models often take this form.  These nonsmooth systems are typically reframed as Filippov systems, a special type of multivalued differential inclusion.  The qualitative properties of these inclusions have been studied over the last few decades, primarily in the context of control systems.  Our interest in these systems is in understanding what behavior identified in the nonsmooth model may be continued to families of smooth differential equations which limit to the Filippov system; determining this information is particularly important in this context because the piecewise-continuous model is frequently considered to be a heuristically understandable approximation of a more realistic smooth system.  In this talk we will examine how Conley index theory may be applied to the study of differential inclusions in order to address this goal.  In particular, we will discuss how attractor-repeller pairs identified in a Filippov system continue to nearby smooth systems.Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Mar 23

11:15am - Zoom
Climate Seminar
TBA
Mon Mar 22

## Topology Seminar

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

Mon Mar 22

## Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Mar 22

## Special Events and Seminars

11:00am - via Zoom https://umn.zoom.us/j/97214138395
HA-GMT-PDE Seminar
Laurel Ohm, Courant Institute
##### Abstract:

Titles and abstracts of the talks will be made available close to each talk at the seminar website https://sites.google.com/view/hagmtpdeseminar. To subscribe to the weekly seminar mailing list, please contact Bruno Poggi Cevallos, at poggi008@umn.edu. The seminar is organized by Bruno Poggi Cevallos (University of Minnesota), Ryan Matzke (University of Minnesota), and José Luis Luna García (University of Missouri).

Fri Mar 19

## IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
The Engineering of Data Science & The Science of Data Engineering
Daniel Kaslovsky, Automox
##### Abstract:

Data Science is a broad and evolving field, offering many opportunities for Applied Math, Computer Science, and Engineering graduates. Delivering a data-driven product to market requires a mix of all of these skills. In this talk, I will discuss data science and data engineering applications in industry, drawing largely from experiences in cyber security and related fields. I will also share some perspectives on entering industry, interviewing, and imposter syndrome.

Dan Kaslovsky is the technical lead for Data Platform & Analytics at Automox, a growing endpoint management startup. Previously, he led a data science team at LogRhythm in designing and implementing machine learning software for information security applications and user behavior modeling. Before moving to industry, Dan was an NSF postdoctoral fellow at NIST and received his Ph.D. in Applied Math from the University of Colorado, Boulder, where he researched high-dimensional data analysis and statistics. Dan lives in the Boulder, CO area and enjoys his family, sports, coding, and coffee.

Fri Mar 19

## MCFAM Seminar

12:00pm - Zoom: https://umn.zoom.us/j/94564033758
Model misspecification, Bayesian versus credibility estimation, and Gibbs posteriors
Liang (Jason) Hong, University of Texas at Dallas
##### Abstract:

In the context of predicting future claims, a fully Bayesian analysis  one that
specifies a statistical model, prior distribution, and updates using Bayess formula  is often viewed as the gold-standard, while Bühlmanns credibility estimator serves as a simple approximation. But those desirable properties that give the Bayesian solution its elevated status depend critically on the posited model being correctly specified. Here we investigate the asymptotic behavior of Bayesian posterior distributions under a misspecified model, and our conclusion is that misspecification bias generally has damaging effects
that can lead to inaccurate inference and prediction. The credibility estimator, on the other hand, is not sensitive at all to model misspecification, giving it an advantage over the Bayesian solution in those practically relevant cases where the model is uncertain. This begs the question: does robustness to model misspecification require that we abandon uncertainty quantification based on a posterior distribution? Our answer to this question is No, and we offer an alternative Gibbs posterior construction. Furthermore, we argue that this Gibbs perspective provides a new characterization of Bühlmanns credibility estimator.

Bio: Liang Hong, PhD, FSA, is an Associate Professor in the Department of Mathematical Sciences at the University of Texas at Dallas. His current research interests are actuarial science and foundations of mathematics. In actuarial science, he is primarily interested in applying machine/statistical learning methods, such as Bayesian non-parametric models, conformal prediction, and Gibbs posteriors, to solve important insurance problems.

Thu Mar 18

## Colloquium

3:30pm - Zoom ID 91514486597 (contact faculty for pw)
Mathematics and physics of moiré patterns
Mitchell Luskin, University of Minnesota, Twin Cities
##### Abstract:

Placing a two-dimensional lattice on another with a small rotation gives rise to periodic "moire" patterns on a superlattice scale much larger than the original lattice. This effective large-scale fundamental domain allows phenomena such as the fractal Hofstadter butterfly spectrum in Harper's equation to be observed in real crystals. Experimentalists have more recently observed new correlated phases at "magic" twist angles predicted by theorists.

We will give mathematical and computational models to predict and gain insight into new physical phenomena at the moiré scale including our recent mathematical and experimental results for twisted trilayer graphene.

Thu Mar 18

11:15am - Zoom
Climate Seminar
TBA
Wed Mar 17

## Probability Seminar

9:00am - via Zoom
Triviality of the geometry of mixed p-spin spherical Hamiltonians with external field
David Belius, University of Basel
##### Abstract:

Isotropic Gaussian random fields on the sphere are paradigmatic high dimensional complex functions. Due to their appearance in spin glass models in statistical physics, they are also known as mixed p-spin spherical Hamiltonians. One manifestation of the complexity is the presence, in general, of an exponentially large number of critical points. In this talk I will present a result stating that in the presence of a deterministic linear term (external field in the physics terminology) with strength above a certain threshold, the geometry of such functions trivializes in the sense that the only critical points of the random function are then one maximum and one minimum.

This extends work of Fyodorov '13, which identified the trivial regime for the special case of pure p-spin Hamiltonians with random external field, and makes mathematically rigorous part of the results of work of Ros et al '19 which derived this claim for pure p-spin Hamiltonians with deterministic external field using physics methods.

Our main tool is the Kac-Rice formula for computing the expected number of critical points of random functions.

Based on joint work with Jiri Cerny, Shuta Nakajima, and Marius Schmidt.

Tue Mar 16

## IMA Data Science Lab Seminar

1:25pm - Zoom
Consistent Sparse Deep Learning: Theory and Computation
Faming Liang, Purdue University
##### Abstract:

Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training, prediction and interpretation. We propose a frequentist-like method for learning sparse DNNs and justify its consistency under the Bayesian framework: the proposed method could learn a sparse DNN with at most $O(n/\log(n))$ connections and nice theoretical guarantees such as posterior consistency, variable selection consistency and asymptotically optimal generalization bounds. In particular, we establish posterior consistency for the sparse DNN with a mixture Gaussian prior, show that the structure of the sparse DNN can be consistently determined using a Laplace approximation-based marginal posterior inclusion probability approach, and use Bayesian evidence to elicit sparse DNNs learned by an optimization method such as stochastic gradient descent in multiple runs with different initializations. The proposed method  is computationally more efficient than standard Bayesian methods for large-scale sparse DNNs.  The numerical results indicate that the proposed method can perform very well for large-scale network compression and high-dimensional nonlinear variable selection, both advancing interpretable machine learning.  The talk is based on a joint work with Yan Sun and Qifan Song.
Faming Liang is Professor of Statistics at Purdue University. Before joining Purdue, he held a faculty position at University of Florida and Texas A&M University. Faming has wide research interests, including machine learning, Monte Carlo methods, bioinformatics, high-dimensional statistics, and big data. He is ASA fellow and IMS fellow, and has published over 120 journal papers.

Tue Mar 16

## Dynamical Systems

12:20pm - via Zoom
Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems
Maximilian Engel, Freie Universität Berlin
##### Abstract:

We confirm a long-standing conjecture concerning shear-induced chaos in stochastically perturbed systems exhibiting a Hopf bifurcation. The method of showing the main chaotic property, a positive Lyapunov exponent, is a computer-assisted proof. Using the recently developed theory of conditioned Lyapunov exponents on bounded domains and the modified Furstenberg-Khasminskii formula, the problem boils down to the rigorous computation of eigenfunctions of the Kolmogorov operators describing distributions of the underlying stochastic process. The proof techniques fall into the category of a posteriori validation methods, meaning that we first compute a numerical approximation of an eigenpair for the operators and then use a fixed point argument to prove the existence of an exact solution nearby obtaining explicit error bounds.

Tue Mar 16

11:15am - Zoom
Climate Seminar
TBA
Mon Mar 15

## Topology Seminar

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

Mon Mar 15

## Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Mar 15

## Special Events and Seminars

11:00am - via Zoom https://umn.zoom.us/j/91471008662
HA-GMT-PDE Seminar
Sean McCurdy, Carnegie Mellon University
##### Abstract:

Titles and abstracts of the talks will be made available close to each talk at the seminar website https://sites.google.com/view/hagmtpdeseminar. To subscribe to the weekly seminar mailing list, please contact Bruno Poggi Cevallos, at poggi008@umn.edu. The seminar is organized by Bruno Poggi Cevallos (University of Minnesota), Ryan Matzke (University of Minnesota), and José Luis Luna García (University of Missouri).

Fri Mar 12

## MCFAM Seminar

12:00pm - Zoom
Rough Volatility
Mathieu Rosenbaum, Ecole Polytechnique
##### Abstract:

The goal of this talk is to introduce rough volatility models. We will demonstrate that this approach significantly outperforms conventional ones, both from a statistical and a risk management viewpoint. We will notably illustrate this showing how this new class of models enables us to solve long standing problems in financial engineering.

Bio: Mathieu Rosenbaum is a full professor at École Polytechnique, where he holds the chair Analytics and Models for Regulation and is co-head of the quantitative finance (El Karoui) master program. His research mainly focuses on statistical finance problems, regulatory issues and risk management of derivatives
He published more than 65 articles on these subjects in the best international journals.
He is notably one of the most renowned experts on the quantitative analysis of market microstructure and high frequency trading. On this topic, he co-organizes every two years in Paris the conference "Market Microstructure, Confronting Many Viewpoints". He is also at the origin (with Jim Gatheral and Thibault Jaisson) of the development of rough volatility models. Mathieu Rosenbaum has collaborations with various financial institutions (investment banks, hedge funds, regulators, exchanges...),
notably BNP-Paribas since 2004. He also has several editorial activities as he is one of the editors in chief of the journal Market Microstructure and Liquidity and is associate editor for 10 other journals.
He received the Europlace Award for Best Young Researcher in Finance in 2014, the European Research Council Grant in 2016, the Louis Bachelier prize in 2020 and the Quant of the Year award in 2021.

Thu Mar 11

11:15am - Zoom
Climate Seminar
TBA
Wed Mar 10

## Probability Seminar

4:00pm - via Zoom
Probability Seminar
TBD
Wed Mar 10

## PDE Seminar

3:35pm - via Zoom
Universal dynamics of pulled fronts
Montie Avery, UMN
##### Abstract:

The formation of structure in spatially extended systems is often mediated by an invasion process, in which a pointwise stable state invades a pointwise unstable state. A fundamental goal is then to predict the speed of this invasion. The marginal stability conjecture postulates that, absent a mechanism through which the nonlinearity enhances propagation, the invasion speed is predicted by marginal linear stability of the pointwise unstable background state in a suitable norm. We introduce a set of largely model-independent conceptual assumptions under which we establish nonlinear propagation at the linear spreading speed, thereby resolving the marginal stability conjecture in the general case of stationary invasion. Our assumptions hold for open classes of parabolic equations, including higher order equations without comparison principles, while previous results rely on special structure of the equation and the presence of a comparison principle. Our result also establishes universality of the logarithmic in time delay in the position of the front, compared with propagation strictly at the linear speed, as predicted in generality by Ebert and van Saarloos and first established in the special case of the Fisher-KPP equation by Bramson. Our proof describes the invasion process through the interaction of a Gaussian leading edge with the pulled front in the wake. Technically, we rely on sharp linear decay estimates to control errors from this matching procedure and corrections from the initial data. https://umn.zoom.us/j/91765959125?pwd=RjRkSW9PNi9HNzVOb2lwb0tkWVVoZz09

Tue Mar 09

## Commutative Algebra Seminar

3:35pm - via Zoom
Extremal Singularities in Positive Characteristic
Janet Page, University of Michigan
##### Abstract:

In this talk, I will introduce an interesting class of polynomials which define the most singular possible (reduced) hypersurfaces in positive characteristic as measured by an invariant called the F-pure threshold. These polynomials have a rich algebraic structure coming from the fact that they have a matrix factorization mirroring the theory of quadratic forms, and there are only finitely many of them in any bounded degree and number of variables (up to a linear change of coordinates). We fully classify them by associating to them directed graphs which capture their combinatorial data. Time permitting, we will apply this theory to see some interesting properties of cubic surfaces in characteristic two.Zoom Link: https://umn.zoom.us/j/96978192398?pwd=ajFBN3BIUFNudHpVdXMrbXF0RUFjQT09Meeting ID: 969 7819 2398Passcode: RingsHave1

Tue Mar 09

11:15am - Zoom
Climate Seminar
TBA
Mon Mar 08

## Topology Seminar

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

Mon Mar 08

## Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Mar 08

## Special Events and Seminars

11:00am - via Zoom https://umn.zoom.us/j/91770370986
HA-GMT-PDE Seminar
Silvia Ghinassi&nbsp;, University of Washington
##### Abstract:

Titles and abstracts of the talks will be made available close to each talk at the seminar website https://sites.google.com/view/hagmtpdeseminar. To subscribe to the weekly seminar mailing list, please contact Bruno Poggi Cevallos, at poggi008@umn.edu. The seminar is organized by Bruno Poggi Cevallos (University of Minnesota), Ryan Matzke (University of Minnesota), and José Luis Luna García (University of Missouri).

Fri Mar 05

## Combinatorics Seminar

3:35pm - via Zoom
P-strict promotion and B-bounded rowmotion
Jessica Striker, TBD
##### Abstract:

We generalize semistandard Young tableaux to P-strict labelings and show that promotion on these objects is in equivariant bijection with a piecewise-linear toggle action on B-bounded labelings of an associated poset, that in many nice cases is conjugate to rowmotion. We apply this result to flagged tableaux, Gelfand-Tsetlin patterns, and symplectic tableaux, obtaining new cyclic sieving and homomesy conjectures

via Zoom id is 941-2794-9847

Fri Mar 05

## IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
Lecture
Tetiana Grinberg, Symbiokinetics Inc
Fri Mar 05

## MCFAM Seminar

12:00pm - Location: Zoom: https://umn.zoom.us/j/9456403375
Cyclical Design for Target Benefit Pension Plan
Xiaobai (Mike) Zhu, Southwestern University of Finance and Economics, China
##### Abstract:

In this paper, we derived the optimal cyclical design of Target Benefit (TB) pension plan. We focused on the stability of the benefit payment, and formulated an optimal control problem using a regime-switching model. We drew a number of remarks to improve the readability of our explicit solution, and made simplifications to enhance the transparency of the risk sharing design. We provided a new yet natural interpretation for a commonly used parameter under the TB context. We highlighted that cautions must be made when studying TB design using optimal control theory. Our numerical result suggested that a 100/0 investment strategies is preferred for the robustness of TB design, and the risk sharing mechanism should include both counter- and pro-cyclical components.

Bio: For my personal information, my full name is Xiaobai Zhu, I am assistant professor at School of Insurance, Southwestern University of Finance and Economics, China, my research interest is on hybrid pension plans and longevity modelling.

Thu Mar 04

## Colloquium

3:30pm - via Zoom ID 91514486597 (contact faculty for pw)
Bessel F-crystals for reductive groups
Xinwen Zhu, California Institute of Technology
##### Abstract:

I will first review the relationship between the classical Bessel differential equation

z^2f''(z)+zf'(z)+zf(z)=0

and the classical Kloosterman sum

\sum_{x=1}^{p-1} e((x+x*)/p), where e(-)=exp(2\pi i -) and x* is the inverse of x mod p

following the work of Deligne, Dwork and Katz. Then I will discuss a generalization of this story from the point of view of Langlands duality, based on the works by Frenkel-Gross, Heinloth-Ngo-Yun, myself, and the recent joint work with Daxin Xu. In particular, the joint work with Xu gives (probably) the first example of a p-adic version of the geometric Langlands correspondence. It allows us to prove a conjecture of Heinloth-Ngo-Yun on the functoriality of some specific automorphism forms.

Thu Mar 04

11:15am - Zoom
Climate Seminar
TBA
Wed Mar 03

## Probability Seminar

4:00pm - via Zoom
On the TAP equations for the Sherrington-Kirkpatrick Model
Christian Brennecke, Harvard University
##### Abstract:

In this talk, I will review the Thouless-Anderson-Palmer (TAP) equations for the classical Sherrington-Kirkpatrick spin glass and present a dynamical derivation, valid at sufficiently high temperature. In our derivation, the TAP equations follow as a simple consequence of the decay of the two point correlation functions. The methods can also be used to establish decay of higher order correlation functions. We illustrate this by proving a suitable decay bound on the three point functions which implies an analogue of the TAP equations for the two point functions. The talk is based on joint work with A. Adhikari, P. von Soosten and H.T. Yau.

Wed Mar 03

## PDE Seminar

3:35pm - via Zoom
Boundary unique continuation of Dini domains
Zihui Zhao, University of Chicago
Wed Mar 03

## PDE Seminar

3:35pm - via Zoom
Boundary unique continuation of Dini domains
Zihui Zhao, University of Chicago
##### Abstract:

Let u be a harmonic function in \Omega \subset \mathbb{R}^d. It is known that in the interior, the singular set \mathcal{S}(u) = \{u=|\nabla u|=0 \} is (d-2)-dimensional, and moreover \mathcal{S}(u) is (d-2)-rectifiable and its Minkowski content is bounded (depending on the frequency of u). We prove the analogue at the boundary for C^1-Dini domains: If the harmonic function u vanishes on an open subset E of the boundary, then near E the singular set \mathcal{S}(u) \cap \overline{\Omega} is (d-2)-rectifiable and has bounded Minkowski content. Dini domain is the optimal domain for which \nabla u is continuous towards the boundary, and in particular every C^{1,\alpha} domain is Dini. The main difficulty is the lack of monotonicity formula for boundary and interior points of a Dini domain. This is joint work with Carlos Kenig.Join Zoom Meetinghttps://umn.zoom.us/j/91765959125?pwd=RjRkSW9PNi9HNzVOb2lwb0tkWVVoZz09Meeting ID: 917 6595 9125Passcode: VinH16

Tue Mar 02

## IMA Data Science Lab Seminar

1:25pm - Zoom
Coordinate Methods for Solving Eigenvalue Problems in High Dimensions
Jianfeng Lu, Duke University
##### Abstract:

The leading eigenvalue problem of a differential operator arises in many scientific and engineering applications, in particular quantum many-body problems. Due to the curse of dimensionality conventional algorithms become impractical due to the huge computational
and memory complexity. In this talk, we will discuss some of our recent works on developing efficient coordinate based approaches for eigenvalue problems in high dimension and on convergence analysis of randomized coordinate algorithms based on the theory of random dynamical systems. (joint work with Ziang Chen, Yingzhou Li, and Zhe Wang)

Jianfeng Lu is a Professor of Mathematics, Physics, and Chemistry at Duke University. Before joining Duke University, he obtained his PhD in Applied Mathematics from Princeton University in 2009 and was a Courant Instructor at New York University from 2009 to 2012. He works on mathematical analysis and algorithm development for problems and challenges arising from computational physics, theoretical chemistry, materials science, high-dimensional PDEs, and machine learning. His work has been recognized by a Sloan Fellowship, a NSF Career Award, and the 2017 IMA Prize in Mathematics and its Applications.

Tue Mar 02

## Dynamical Systems

12:20pm - via Zoom
Synchronization of clocks and metronomes: A perturbation analysis based on multiple timescales
##### Abstract:

In 1665, Huygens observed that two pendulum clocks hanging from the same board became synchronized in antiphase after hundreds of swings. On the other hand, modern experiments with metronomes placed on a movable platform show that they often tend to synchronize in phase, not antiphase. Here we study both in-phase and antiphase synchronization in a model of pendulum clocks and metronomes and analyze their long-term dynamics with the tools of perturbation theory.  Specifically, we exploit the separation of timescales between the fast oscillations of the individual pendulums and the much slower adjustments of their amplitudes and phases. By scaling the equations appropriately and applying the method of multiple timescales, we derive explicit formulas for the regimes in parameter space where either antiphase or in-phase synchronization are stable, or where both are stable. Although this sort of perturbative analysis is standard in other parts of nonlinear science, it has been applied surprisingly rarely in the context of Huygens's clocks. Unusual features of our approach include its treatment of the escapement mechanism, a small-angle approximation up to cubic order, and both a two- and three-timescale asymptotic analysis.

Tue Mar 02

11:15am - Zoom
Climate Seminar
TBA
Mon Mar 01

## Topology Seminar

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

Mon Mar 01

## Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Mar 01

## Special Events and Seminars

11:00am - via Zoom https://umn.zoom.us/j/98087789433
HA-GMT-PDE Seminar
&nbsp;&nbsp;Polona Durcik, Chapman University)
##### Abstract:

Titles and abstracts of the talks will be made available close to each talk at the seminar website https://sites.google.com/view/hagmtpdeseminar. To subscribe to the weekly seminar mailing list, please contact Bruno Poggi Cevallos, at poggi008@umn.edu. The seminar is organized by Bruno Poggi Cevallos (University of Minnesota), Ryan Matzke (University of Minnesota), and José Luis Luna García (University of Missouri).

Fri Feb 26

## IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
Data Science at The New York Times
Chris Wiggins, Columbia University
##### Abstract:

The Data Science group at The New York Times develops and deploys machine learning solutions to newsroom and business problems. Re-framing real-world questions as machine learning tasks requires not only adapting and extending models and algorithms to new or special cases but also sufficient breadth to know the right method for the right challenge.

I'll first outline how unsupervised, supervised, and reinforcement learning methods are increasingly used in human applications for; description, prediction, and prescription, respectively.

I'll then focus on the 'prescriptive' cases, showing how methods from the reinforcement learning and causal inference literatures can be of direct impact in; engineering, business, and decision-making more generally.

Chris Wiggins is an Associate Professor of Applied Mathematics at Columbia University and the Chief Data Scientist at The New York Times.

At Columbia he is a founding member of the executive committee of the Data Science Institute, and of the Department of Applied Physics and Applied Mathematics as well as the Department of Systems Biology, and is affiliated faculty in Statistics.

He is a co-founder and co-organizer of hackNY (http://hackNY.org), a nonprofit which since 2010 has organized once a semester student hackathons and the hackNY Fellows Program, a structured summer internship at NYC startups.

Prior to joining the faculty at Columbia he was a Courant Instructor at NYU (1998-2001) and earned his PhD at Princeton University (1993-1998) in Theoretical Physics.

He is currently writing a book on the history and ethics of data with Professor Matt Jones (Columbia) forthcoming from W. W. Norton & Company in 2021. He is a Fellow of the American Physical Society and is a recipient of Columbia's Avanessians Diversity Award.

chrishwiggins

Email to be shared:
chris.wiggins@gmail.com

Fri Feb 26

## MCFAM Seminar

9:00am - Zoom: https://umn.zoom.us/j/94564033758
MCFAM Seminar Canceled - Deep Learning Models of High-Frequency Financial Data
Justin Sirignano, University of Illinois at Urbana-Champaign
##### Abstract:

We develop and evaluate deep learning models for predicting price movements in high-frequency data. Deep recurrent networks are trained on a large limit order book dataset from hundreds of stocks across multiple years. Several data augmentation methods to reduce overfitting are analyzed. We also develop and evaluate deep reinforcement learning models for optimal execution problems with limit order book data. "Optimal execution" is the problem of formulating, given an a priori determined order direction (buy or sell) and order size, the optimal adaptive submission strategy to complete the order at the best possible price(s).The performance of deep recurrent models is compared against other types of models trained with reinforcement learning, such as linear VAR models and feedforward neural networks.

Bio: Justin Sirignano is an Associate Professor at the Mathematical Institute at the University of Oxford, where he is a member of the Mathematical & Computational Finance and Data Science groups. He received his PhD from Stanford University and was a Chapman Fellow at the Department of Mathematics at Imperial College London. His research interests are in the areas of applied mathematics, machine learning, and computational methods.

Thu Feb 25

## Colloquium

3:30pm - Via Zoom ID 91514486597 (contact faculty for pw)
From Grassmannians to Catalan numbers
Thomas Lam, University of Michigan, Ann Arbor
##### Abstract:

The binomial coefficients have a well-studied q-analogue known as Gaussian polynomials. These polynomials appear as Poincare polynomials (or point counts) of the Grassmannian of k-planes in C^n (or F_q^n).

Another family of important combinatorial numbers is the Catalan numbers, and they have two well-studied q-analogues from the 1960s, due to Carlitz and Riordan and to MacMahon respectively. I will explain how these q-analogues appear as the Poincare polynomial and point count, respectively, of an open (non-compact) subvariety of the Grassmannian known as the top positroid variety. The story involves connections to knot theory and to the geometry of flag varieties.

The talk is based on joint work with Pavel Galashin.

Thu Feb 25

11:15am - Zoom
Climate Seminar
TBA
Wed Feb 24

## Probability Seminar

4:00pm - via Zoom
Further Simplifying the Glass Problem
Patrick Charbonneau, Duke University
##### Abstract:

The random Lorentz gas (RLG) is a minimal model of both transport in heterogenous media and structural glasses. Yet these two perspectives are fundamentally inconsistent, as the dynamical arrest is continuous in the former and discontinuous in the latter. This tension hinders our understanding of either phenomenon, as well as of the RLG itself. By considering an exact solution of the RLG in the infinite- dimensional d ? ? limit as well as numerics in d = 2 . . . 20 we here resolve this paradox. Our results reveal the importance of instantonic corrections, related to rare cage escapes, in unifying glass and percolation physics. This advance suggests a starting point for a first-principle description of hopping processes in structural glasses. We also conjecture tighter formal bounds on the asymptotic d ? ? RLG percolation threshold, which may further enlighten our understanding of that model.

Tue Feb 23

## Commutative Algebra Seminar

3:35pm - via Zoom
Uniform Asymptotic Growth of Symbolic Powers of Ideals
Robert Walker&nbsp;, University of Wisconsin
##### Abstract:

Algebraic geometry (AG) is a major generalization of linear algebra which is fairly influential in mathematics. Since the 1980's with the development of computer algebra systems like Mathematica, AG has been leveraged in areas of STEM as diverse as statistics, robotic kinematics, computer science/geometric modeling, and mirror symmetry. Part one of my talk will be a brief introduction to AG, to two notions of taking powers of ideals (regular vs symbolic) in Noetherian commutative rings, and to the ideal containment problem that I study in my thesis. Part two of my talk will focus on stating the main results of my thesis in a user-ready form, giving a "comical" example or two of how to use them. At the risk of sounding like Paul Rudd in \textit{Ant-Man}, I hope this talk will be awesome.A first course in AG would be helpful but I review what I need for my thesis problem.Zoom Link: https://umn.zoom.us/j/96978192398?pwd=ajFBN3BIUFNudHpVdXMrbXF0RUFjQT09Meeting ID: 969 7819 2398Passcode: RingsHave1

Tue Feb 23

## IMA Data Science Lab Seminar

1:25pm - Online
Ultrametric Gromov-Hausdorff and Gromov-Wasserstein Distances
Facundo Mémoli, The Ohio State University
##### Abstract:

The Gromov-Hausdorff (GH) distance provides a flexible notion of dissimilarity between datasets. It is known that computing the GH distance between finite metric spaces leads to NP-Hard computational problems. This is true even for finite ultrametric spaces, which are highly structured metric spaces satisfying the so-called 'strong' triangle inequality. We identify a one-parameter family of Gromov-Hausdorff-like distances dGH_p between finite metric spaces, for p \in [1,\infty], with the property that dGH_1 is the standard GH distance (and therefore NP-hard to compute) whereas, surprisingly, the case p=\infty yields a notion of distance  between ultrametric spaces which is computable in polynomial time on the cardinality of the inputs. This distance is itself an ultrametric on the collection of all ultrametric spaces.  Ultrametric spaces are widespread in applications and are, in particular, the standard output type of hierarchical clustering algorithms (in the form of dendrograms).

This talk will overview these and related results and will also describe an analogous construction based on optimal transport which leads to interesting computational alternatives.

Facundo Mémoli is a professor in the Department of Mathematics and in the Department of Computer Science and Engineering at the Ohio State University. Facundo obtained his PhD at the University of Minnesota in 2005, he was then a postdoc at Stanford, and joined OSU as a faculty in 2013. His research interests include topics in the intersection of metric geometry, topology, optimal transport, and applications to science and engineering such as topological data analysis, and networks.

Tue Feb 23

11:15am - Zoom
Climate Seminar
TBA
Mon Feb 22

## Topology Seminar

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

Mon Feb 22

## Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Feb 22

## Special Events and Seminars

11:00am - via Zoom https://umn.zoom.us/j/92095338432
HA-GMT-PDE Seminar
Blair Davey&nbsp;, Montana State University
##### Abstract:

Titles and abstracts of the talks will be made available close to each talk at the seminar website https://sites.google.com/view/hagmtpdeseminar. To subscribe to the weekly seminar mailing list, please contact Bruno Poggi Cevallos, at poggi008@umn.edu. The seminar is organized by Bruno Poggi Cevallos (University of Minnesota), Ryan Matzke (University of Minnesota), and José Luis Luna García (University of Missouri).

Fri Feb 19

## Combinatorics Seminar

3:35pm - via Zoom ID is 941-2794-9847
T-path Formula for Decorated Super-Teichmuller Spaces
Sylvester Zhang, UMN
##### Abstract:

Penner's lambda-lengths of a decorated Teichmuller space on a marked disk form a type A Cluster algebra, and recently, a supersymmetric version of the decorated Teichmuller theory was introduced by Penner and Zeitlin. In this talk, I will investigate the super lambda-lengths coming from a marked disk, and give a combinatorial formula extending Schiffler's T-path formula for Type A Cluster algebras. I will discuss the connection between the super lambda-lengths and super frieze patterns of Morier-Genoud--Ovsienko--Tabachnikov. And lastly, I will also discuss how our formula relates to cluster superalgebras, a notion which is still partially understood. This talk is based on joint work with Gregg Musiker and Nick Ovenhouse.

Fri Feb 19

## IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
Cyber Security: A New Front for Computational Science and Engineering
Ali Pinar, Sandia National Laboratories
##### Abstract:

Securing cyber systems is paramount, but cyber defenders lack evidence-based techniques required to make high-consequence decisions.  With lack of principled and rigorous measurements and models, cyber defenders resort to heuristics and expert intuitions.

Cyber experimentation is commonly used in security, and we approach this problem as a new front in computation science and engineering.   We use cyber emulation as a predictive capability and support this capability with uncertainty quantification (UQ) techniques to verify experiments, incorporate uncertainties in experiments for rigorous experimentation.  Finally, we use adversarial optimization to improve our defenses.

The cyber systems are different from physics-based systems for which many UQ and optimization techniques were developed, and thus we need novel approaches.  This talk will summarize our  progress on this problem and point to  the new challenges we are facing.

Fri Feb 19

## MCFAM Seminar

12:00pm - Zoom: https://umn.zoom.us/j/94564033758
Static and semi-static hedging as contrarian or conformist bets
Sergei Levendorskii
##### Abstract:

Once the costs of maintaining the hedging portfolio are properly takeninto account, semi-static portfolios should more properly be thought of as separate classes of derivatives, with non-trivial, model-dependent payoff structures. We derive new integral representations for payoffs of exotic European options in terms of payoffs of vanillas, different from the Carr-Madan representation, and suggest approximations of the idealized static hedging/replicating portfolio using vanillas available in the market. We study the dependence of the hedging error on a model used for pricing and show that the variance of the hedging errors of static hedging portfolios can be sizably larger than the errors of variance-minimizing portfolios. We explain why the exact semi-static hedging of barrier options is impossible for processes with
jumps, and derive general formulas for variance-minimizing semi-static portfolios. We show that hedging using vanillas only leads to larger errors than hedging using vanillas and first touch digitals. In all cases, efficient calculations of the weights of the hedging portfolios are in the dual space using new efficient numerical methods for calculation of the Wiener-Hopf factors and
Laplace-Fourier inversion.

Bio:Dr. Levendorskii is a founding partner at Calico Science Consulting in Austin TX. Dr. Levendorskii has developed several models and methods used by the financial services industry. His areas of expertise are Lévy processes with heavy and semi-heavy tails, Financial Mathematics, Real Options, Stochastic Optimization, Applied Fourier Analysis, Spectral Theory, Degenerate Elliptic Equations, Pseudo-differential operators, Numerical methods, Insurance, Quantum Groups, and Fractional Differential Equations. Prior to Calico, he was Chair in Financial Mathematics and Actuarial Sciences, Department of Mathematics and Deputy Director of Institute of Finance, University of Leicester, United Kingdom. He holds a Doctor of Sciences in Mathematics from Academy of Sciences of the Ukraine and he also earned a PhD in Mathematics from Rostov State University."

Thu Feb 18

## Colloquium

5:00pm - Via Zoom ID 91514486597 (contact faculty for pw)
Wild ramification and cotangent bundle in mixed characteristic
Takeshi Saito, University of Tokyo
##### Abstract:

As an algebraic analogue of micro local analysis, the singular support and characteristic of an etale sheaf on a smooth algebraic variety over a perfect field is defined on the cotangent bundle. We discuss this geometric theory and some recent progress in the arithmetic context.

Thu Feb 18

11:15am - Zoom
Climate Seminar
TBA
Wed Feb 17

## Probability Seminar

4:00pm - via Zoom
The heat and the landscape
Bálint Virág, University of Toronto
##### Abstract:

If lengths 1 and 2 are assigned randomly to each edge in the planar grid, what are the fluctuations of distances between far away points?

This problem is open, yet we know, in great detail, what to expect.

The directed landscape, a universal random plane geometry, provides the answer to such questions.

In some models, such as directed polymers, the stochastic heat equation, or the KPZ equation, random plane geometry hides in the background.

Principal component analysis, a fundamental statistical method, comes to the rescue: BBP statistics can be used to show that these models converge to the directed landscape.

Wed Feb 17

## PDE Seminar

3:35pm - via Zoom
Global Existence for the 3D Muskat problem
Stephen Cameron, NYU-Courant
##### Abstract:

The Muskat problem studies the evolution of the interface between two incompressible, immiscible fluids in a porous media. In the case that the fluids have equal viscosity and the interface is graphical, this system reduces to a single nonlinear, nonlocal parabolic equation for the parametrization. Even in this stable regime, wave turning can occur leading to finite time blowup for the slope of the interface. Before that blowup though, we prove that an imperfect comparison principle still holds. Using this, we are able to show that solutions exist for all time so long as either the initial slope is not too large, or the slope stays bounded for a sufficiently long time. Join Zoom Meetinghttps://umn.zoom.us/j/91765959125?pwd=RjRkSW9PNi9HNzVOb2lwb0tkWVVoZz09Meeting ID: 917 6595 9125Passcode: VinH16

Tue Feb 16

## IMA Data Science Lab Seminar

1:25pm - Zoom
Learning the Manifold of Molecular Structures in Cryo-EM
Joakim Anden, Royal Institute of Technology (KTH)
##### Abstract:

Cryogenic electron microscopy (cryo-EM) is an imaging method wherein a solution containing biological macromolecules is frozen in a thin layer of ice and imaged in a transmission electron microscope. The resulting tomographic projections are then assembled into density maps depicting the 3D structure of the molecule. While many molecules can be forced to take on a fixed 3D structure, this is not always the case. Indeed, examining the structural variability of the molecule is often critical to understanding its dynamics and function.
We propose a new method for examining this variability by modeling the set of 3D structures as a low-dimensional manifold in the space of density maps. We first estimate the linear subspace which captures most of the 3D variability in the dataset. By restricting maps to this subspace, we may then create low-resolution 3D reconstructions from each image. These are in turn used to construct a graph Laplacian over the set of images, whose eigenvectors characterize the underlying low-dimensional manifold. These eigenvectors, known as spectral volumes, may then be used to study the topology of the manifold, but also to examine the principal modes of variability and create higher-resolution 3D reconstructions.

Joakim Andén received his M.Sc. degree in mathematics from the Université Pierre et Marie Curie, Paris, France, in 2010 and his Ph.D. degree in applied mathematics from École Polytechnique, Palaiseau, France, in 2014.
His doctoral work consisted of studying the invariant scattering transform applied to time series, such as audio and medical signals, in order to extract information relevant to classification and other tasks.
Between 2014 and 2017, he was a postdoctoral researcher with the Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, USA, where his research focused on reconstruction algorithms for electron cryomicroscopy.
From 2017 to 2020 he worked as a research scientist with the Center for Computational Mathematics, Flatiron Institute, New York, NY, USA, a division of the Simons Foundation.
He is currently an associate professor at the Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden.
His research interests include signal processing, machine learning, and inverse problems.

Tue Feb 16

## Dynamical Systems

12:20pm - via Zoom
Locked fronts in a discrete time discrete space population model
Matt Holzer, George Mason University
##### Abstract:

We study locked invasion fronts in a model of population dynamics where both space and time are taken to be discrete variables. Locked fronts propagate with rational speed and are observed to persist as system parameters are varied. We construct locked fronts for a particular piecewise linear reproduction function. These fronts are shown to be linear combinations of exponentially decaying solutions to the linear system near the unstable state. We derive conditions on system parameters for which locking occurs and compare our predictions to observations in direct numerical simulations. We obtain leading order expansions for the locking regions in the limit as the migration parameter tends to zero. Strict spectral stability in exponentially weighted spaces is also established.

Tue Feb 16

11:15am - Zoom
Climate Seminar
TBA
Mon Feb 15

## Topology Seminar

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

Mon Feb 15

## Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Feb 15

## Special Events and Seminars

11:00am - via Zoom https://umn.zoom.us/j/95248478720
HA-GMT-PDE Seminar
Georgios Ntosidis, Charles University at Prague
##### Abstract:

Titles and abstracts of the talks will be made available close to each talk at the seminar website https://sites.google.com/view/hagmtpdeseminar. To subscribe to the weekly seminar mailing list, please contact Bruno Poggi Cevallos, at poggi008@umn.edu. The seminar is organized by Bruno Poggi Cevallos (University of Minnesota), Ryan Matzke (University of Minnesota), and José Luis Luna García (University of Missouri).

Fri Feb 12

## IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
Discovering Genetic Networks Using Compressive Sensing
Matthew Herman, Fourier Genetics
##### Abstract:

Consider a particular quantitative trait, and suppose we want to discover a function that maps how n participating genes (or even environmental influences) interact to express the trait. Under plausible assumptions of how they evolved, certain traits can be viewed as  “smooth” functions on the n-dimensional Boolean lattice of possible genomes. This allows approximation of their Fourier transforms, i.e., their gene networks, as sparse, dominated by “low-frequency” components.

In turn, we can use compressive sensing theory to record the trait values from relatively few genomes, yet achieve accurate recovery of the gene network. Work is currently underway to see if empirical data fit the proposed model. If so, it could offer a radical reduction in the number of measurements — from exponential to polynomial in some cases — necessary to quantify the relationship between genomes and certain traits.

In the talk, we will review the Fourier theory connecting quantitative traits and their network of gene interactions, with both concrete and theoretical examples to motivate the idea of “low-level concentration.” If time permits, we will present new results from a trait data set of mouse myopia.

Matthew Herman is Chief Research Scientist at Fourier Genetics in Austin, TX. From 2011 to 2018 he was Senior Algorithm Engineer at InView Technology Corporation, doing R&D on the “single-pixel camera.” He received a Ph.D. in Applied Mathematics in 2009 from the University of California, Davis, focusing on applications of compressive sensing, such as radar and mismatches in the model of the sensing/system matrix — his work on radar was recognized with the 2013 Best Paper Award from the IEEE Signal Processing Society. In his spare time Matt plays the drums in different bands in Austin.

Fri Feb 12

## MCFAM Seminar

12:00pm - Zoom: https://umn.zoom.us/j/94564033758
A machine learning-driven crude oil data analysis, with applications in continuous-time quadratic hedging
Indranil SenGupta, North Dakota State University
##### Abstract:

In this presentation, a refined Barndorff-Nielsen and Shephard (BN-S) model is implemented to find an optimal hedging strategy for commodity markets. The refinement of the BN-S model is obtained through various machine and deep learning algorithms. The refinement leads to the extraction of a deterministic parameter from the empirical data set. The analysis is implemented to the Bakken crude oil data and the aforementioned deterministic parameter is obtained for a wide range of data sets. With the implementation of this parameter in the refined model, it is shown that the resulting model performs much better than the classical stochastic models.

Short bio: Indranil SenGupta is an Associate Professor at the Department of Mathematics at North Dakota State University (NDSU). He is currently the mathematics graduate program director at NDSU. He received his Ph.D. in mathematics from Texas A&M University in 2010. His research interests include mathematical finance, stochastic processes, and data-science. He was the Associate Editor-in-Chief of the journal Mathematics, 2014-2019. Currently, he is an associate editor in the area of finance and risk management for the Journal of Modelling in Management. He is in the editorial board for several other journals.

Thu Feb 11

## Colloquium

3:30pm - Via Zoom ID 91514486597 (contact faculty for pw)
The quartic integrability and long time existence of steep water waves in 2d
Sijue Wu, University of Michigan, Ann Arbor
##### Abstract:

It is known since the work of Dyachenko & Zakharov in 1994 that for the weakly nonlinear 2d infinite depth water waves, there are no 3-wave interactions and all of the 4-wave interaction coefficients vanish on the resonant manifold. In this talk I will present a recent result that proves this partial integrability from a different angle. We construct a sequence of energy functionals $\mathfrak E_j(t)$, directly in the physical space, that involves material derivatives of order $j$ of the solutions for the 2d water wave equation, so that $\frac{d}{dt} \mathfrak E_j(t)$ is quintic or higher order. We show that if some scaling invariant norm, and a norm involving one spacial derivative above the scaling of the initial data are of size no more than $\varepsilon$, then the lifespan of the solution for the 2d water wave equation is at least of order $O(\varepsilon^{-3})$, and the solution remains as regular as the initial data during this time. If only the scaling invariant norm of the data is of size $\varepsilon$, then the lifespan of the solution is at least of order $O(\varepsilon^{-5/2})$. Our long time existence results do not impose size restrictions on the slope of the initial interface and the magnitude of the initial velocity, they allow the interface to have arbitrary large steepnesses and initial velocities to have arbitrary large magnitudes.

Thu Feb 11

11:15am - Zoom
Climate Seminar
TBA
Wed Feb 10

## Probability Seminar

9:00am - via Zoom
The height of Mallows trees
##### Abstract:

Mallows trees are the search trees corresponding to Mallows permutations. Mallows permutations are a parameterized family of random permutations interpolating between the uniformly random permutation and the identity permutation. The corresponding search trees interpolate between random binary search trees and paths. I'll present what we know about the height and structure of such trees, as well as future research possibilities on the subject.
The talk is based on joint work with my doctoral student, Benoît Corsini.

Tue Feb 09

## Commutative Algebra Seminar

3:35pm - via Zoom
The BGG correspondence for toric varieties
Michael Brown&nbsp;, Auburn University
##### Abstract:

This is ongoing joint work with David Eisenbud, Daniel Erman, and Frank-Olaf Schreyer. The Bernstein-Gel'fand-Gel'fand (BGG) correspondence is a derived equivalence between a standard graded polynomial ring and its Koszul dual exterior algebra. One of the many important applications of the BGG correspondence is an algorithm, due to Eisenbud-Fløystad-Schreyer, for computing the cohomology of sheaves on projective space that is, in some cases, the fastest available. The goal of this talk is to discuss a generalization of the BGG correspondence from standard graded to multigraded polynomial rings and how one can use it to develop an Eisenbud-Fløystad-Schreyer-type algorithm for computing sheaf cohomology over projective toric varieties. I will also discuss how we can apply our results to give a proof of a conjecture of Berkesch-Erman-Smith concerning the length of virtual resolutions over toric varieties.Zoom Link: https://umn.zoom.us/j/96978192398?pwd=ajFBN3BIUFNudHpVdXMrbXF0RUFjQT09Meeting ID: 969 7819 2398Passcode: RingsHave1

Tue Feb 09

## IMA Data Science Lab Seminar

1:25pm - Zoom
Using Telco Data to Fight Epidemics
Kenth Monsen, Telenor Research
##### Abstract:

In this talk we will discuss telecom data to estimate human mobility at country-wide scales, and the utilization of such data to better understand the spread of infectious diseases like dengue, malaria and covid-19. This will further be complemented with insights and experiences gathered on privacy, data security, and the need to align solutions with national public health initiatives.

Kenth Engø-Monsen, PhD, is a senior research scientist and data scientist in Telenor Research. He is currently leading Telenor Group’s initiative on big data for social good. With more than 15 years of experience in telecom, Dr. Engø-Monsen has extensive knowledge in the field of telecom data, social network analysis, and applied research using mobile data. He is the co-inventor on numerous patents, has published numerous academic papers in mathematics, computer science, data science, and social science. He received his Master’s in 1995 in Industrial Mathematics from NTNU, Trondheim, Norway, and PhD in 2000 in Computer Science from University of Berge, Norway.

Tue Feb 09

11:15am - Zoom
Climate Seminar
TBA
Mon Feb 08

## Topology Seminar

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

Mon Feb 08

## Topology Seminar

2:30pm - Vincent Hall 311
Topology Seminar

Mon Feb 08

## Special Events and Seminars

11:00am - via Zoom https://umn.zoom.us/j/91341120335
HA-GMT-PDE Seminar
##### Abstract:

Titles and abstracts of the talks will be made available close to each talk at the seminar website https://sites.google.com/view/hagmtpdeseminar. To subscribe to the weekly seminar mailing list, please contact Bruno Poggi Cevallos, at poggi008@umn.edu. The seminar is organized by Bruno Poggi Cevallos (University of Minnesota), Ryan Matzke (University of Minnesota), and José Luis Luna García (University of Missouri).

Fri Feb 05

## Combinatorics Seminar

3:35pm - via Zoom ID is 941-2794-9847
Analyzing Power Grid Stability via the Dragon Marriage Theorem
Rob Davis, Colgate University
##### Abstract:

One real-life situation application of graph theory is the study of electrical grids: they have to be constructed carefully since unstable grids can lead to brownouts, blackouts, damaged equipment, or other possible problems. If we know the connections in the grid that we want, how can the voltages at each node be coordinated in a way that makes sure the network stays stable? This is a difficult question, but even knowing the number of ways to keep a network stable can help.In this talk, we will see how to count the number of "stable solutions" using discrete geometric and algebraic methods. These methods will help us obtain recurrences for networks satisfying mild conditions. Consequently, we obtain explicit, non-recursive formulas for the number of stable solutions for a large class of outerplanar graphs, and conjecture that the formula holds for all outerplanar graphs. Key to these results is the Dragon Marriage Theorem: a generalization of Hall's Matching Theorem with far-reaching implications.

Fri Feb 05

## IMA/MCIM Industrial Problems Seminar

1:25pm - Zoom
Manufacturing Pitfalls to Avoid in Commercialization
Angelique Johnson, MEMStim LLC
##### Abstract:

Disruptive and life changing technologies are created every day in University labs. Unfortunately, most of them will end up in the “valley-of-death.” Why? Because everything that is created must be made. In this talk Dr. Angelique Johnson will highlight how to avoid the ever-expanding pit of University technologies that never make it to commercialization. Spoiler alert! It starts by considering manufacturing at the beginning of the innovation process and not the end.

As founder of MEMStim LLC, I have been driving its commercialization efforts and success. Through my efforts the company has been awarded NSF ICORPS, NIH Phase I/II and EPSCoR grants, as well as several national business plan prizes. I have developed commercial ready technology that has acquired two approved US patents and several international approvals and filings. Over 100 MEMStim arrays have been tested in animal models, and a smaller number in pre-clinical human cadaver trials. The technology has been demoed by leading implant manufacturers. I have formed key strategic relationships with the top three cochlear implant manufacturers that have resulted in LOI's highlighting their eagerness to adopt MEMStim technology and interest in investing in further commercialization.

Fri Nov 22

## Combinatorics Seminar

3:30pm - Vincent Hall 570
A Pieri rule for key polynomials
##### Abstract:

The Pieri rule for the product of a Schur function and a single row Schur function is notable for having an elegant bijective proof that can be intuited by the rules concise diagrammatic interpretation, to wit, by appending cells to a Young diagram. Now, key polynomials generalize Schur polynomials to a basis of the full polynomial ring, in which they also refine the Schubert basis via a nice formula. In this talk, I will describe a Pieri rule for the product of a key polynomial and a single row key polynomial that can be analogously interpreted as appending cells to a key diagram, albeit potentially dropping some cells in between each cell addition. I will also outline the main points of the rules bijective proof, and in the process hopefully illustrate the utility of understanding the rule from a diagrammatic perspective. Joint work with Sami Assaf.

Fri Nov 22

## Special Events and Seminars

3:30pm - Vincent Hall 20
Mass Scale Image Analysis For Automated Plant Phenotyping and Classification via Machine Learning
Riley O'Neill, University of St. Thomas
##### Abstract:

The capacity to quantify crop architecture and morphology is foundational to the development of higher yielding cultivars via hybridization and genetic engineering. However, at the mass scale required by the science, manual plant phenotyping with physical instruments is arduous, time consuming, subjective, and a leading cause of undergraduate burnout in the UMN plant genetics department. While the process has been slightly improved with manual image analysis, such is almost as time consuming and remains subject to human error. Thereby, in efforts to further expedite phenotyping processes, circumvent human error, and provide more detailed analyses, we aim to completely automate plant phenotyping processes for the UMN plant genetics department and beyond. Working from over 15,000 soybean plants, weve advanced robust image processing platforms for measuring petiole and stem length, leaf area, leaf shape via signature curves, and branch angles via energy minimization in 2D, and begun preliminary work at 3D reconstructions from 2D data for 3D branch angles and further analyses. After data extraction and verification, we plan to implement clustering algorithms and machine learning to automatically group plant phenotypes as well as conduct principal component analysis to assemble an allometry space and identify the primary genes of influence.

Fri Nov 22

## AMAAZE

3:30pm - Vincent Hall 20
Mass Scale Image Analysis For Automated Plant Phenotyping and Classification via Machine Learning
Riley O'Neill, University of St. Thomas
##### Abstract:

The capacity to quantify crop architecture and morphology is foundational to the development of higher yielding cultivars via hybridization and genetic engineering. However, at the mass scale required by the science, manual plant phenotyping with physical instruments is arduous, time consuming, subjective, and a leading cause of undergraduate burnout in the UMN plant genetics department. While the process has been slightly improved with manual image analysis, such is almost as time consuming and remains subject to human error. Thereby, in efforts to further expedite phenotyping processes, circumvent human error, and provide more detailed analyses, we aim to completely automate plant phenotyping processes for the UMN plant genetics department and beyond. Working from over 15,000 soybean plants, weve advanced robust image processing platforms for measuring petiole and stem length, leaf area, leaf shape via signature curves, and branch angles via energy minimization in 2D, and begun preliminary work at 3D reconstructions from 2D data for 3D branch angles and further analyses. After data extraction and verification, we plan to implement clustering algorithms and machine learning to automatically group plant phenotypes as well as conduct principal component analysis to assemble an allometry space and identify the primary genes of influence.

Fri Nov 22

## Probability Seminar

2:30pm - Vincent Hall 311
Spherical spin glass models
Eliran Subag, New York University
##### Abstract:

How many critical points does a smooth random function on a high-dimensional space typically have at a given height? how are their distances distributed? what is the volume or geometry of the level sets? can we design efficient optimization algorithms for the random function? For the spherical spin glass models, those questions are closely related to the structure of the Gibbs measures, which have been extensively studied in physics since the 70s.

I will start with an overview of the celebrated Parisi formula and ultrametricity property. I will then describe an alternative method to analyze the Gibbs measure using critical points, in the setting of the pure spherical models. Finally, I will explain how the latter can be extended to all spherical models, using another (soft) geometric approach, while at the same time making rigorous and generalizing the famous Thouless-Anderson-Palmer approach from physics.

Fri Nov 22

## Math Biology Seminar

2:30pm - VinH 209
Math Biology Seminar

Fri Nov 22

## Reading Seminar on Automorphic Forms

1:30pm - Vincent Hall 1

Fri Nov 22

## Special Events and Seminars

1:25pm - Vincent Hall 213
"p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions
TBA
Fri Nov 22

## IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Machine Learning Problems at Target
Mauricio Flores, Target Corporation
##### Abstract:

PhD and Master's students would likely benefit the most from this talk. There will be some discussion on opportunities at Target.

The introduction of this talk will provide an overview of the AI sciences organization at Target and discuss summer internship opportunities. The remainder of the talk will overview the kinds of machine learning problems Target deals with, and dive into three such problems, in the fields of recommender systems and computer vision.

Mauricio Flores received his PhD in Applied Mathematics from the University of Minnesota in 2018, under the supervision of Jeff Calder & Gilad Lerman. He is currently a Lead AI Scientist at Target, where he builds machine learning as well as computer vision models for visually compatible recommendations, and more recently, for damage detection in Targets distribution centers.

Thu Nov 21

## Student Combinatorics Seminar

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

Thu Nov 21

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Nov 21

## Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
Erika Ordog, Duke University
Thu Nov 21

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Geometry of degenerating Calabi-Yau manifolds
Ruobing Zhang, Stony Brook
##### Abstract:

This talk concerns a family of "collapsing" Ricci-flat Kähler manifolds, namely Calabi-Yau manifolds, converging to a lower dimensional limit, which develop singularities arising in various contexts such as metric Riemannian geometry, complex geometry and degenerating nonlinear equations. A primary aspect is to formulate how well behaved or badly behaved such spaces can be in terms of the recently developed regularity theory. Under the above framework, our next focus is on a longstanding fundamental problem which is to understand singularities of collapsing Ricci-flat metrics along an algebraically degenerating family. We will give accurate characterizations of such metrics and explain possible generalizations.

Thu Nov 21

## Topology Seminar

7:00am - Skybox
LOWER (Legs + Butt) @ Skybox - Skybox

##### Abstract:

https://www.fitmetrix.io/webportal/schedulemobile/f9719b20-4914-e911-a97...(Legs%20%2B%20Butt)&dateRangeFrom=2019-11-21T07%3A00%3A00&dateRangeTo=2019-11-21T07%3A55%3A00&locationid=5854&classID=31918145

Wed Nov 20

## Student Number Theory Seminar

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

Wed Nov 20

## PDE Seminar

3:35pm - Vincent Hall 570
Effective Poisson equation of density functional theory at positive temperature
Li Chen, MIT
##### Abstract:

Density functional theory (DFT) has been a very successful effective theory of many-body quantum mechanics. In particular, the Kohn-Sham (KS) equations of DFT serve as an accurate model for the electron densities. The KS equations are a case of the Schrodinger-Poisson equations whose electron-electron effective interaction potential only depends on the density of electrons. When the number of electrons are limited, the KS equation can be solved quickly by numerical method at temperature T = 0. Since physically interesting settings are at T > 0, we study the KS equations at positive temperature and give an iterative scheme to construct solutions.

One important class of electronic structures described by the KS equations is a crystalline lattice. At positive temperature, we show that a local perturbation to a crystalline structure induces an electric field governed by the Poisson equation. The latter equation emerges as an effective equation of the KS equations. This is a joint work with Israel M. Sigal.

Wed Nov 20

## Automorphic Forms and Number Theory

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

Tue Nov 19

## Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Nov 19

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Nov 19

## Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Nov 19

## Colloquium

2:30pm - Vincent Hall 16
Random matrix theory and supersymmetry techniques
Tatyana Shcherbyna, Princeton University
##### Abstract:

Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a spacial structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY) . SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width.

Tue Nov 19

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Nov 19

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Robust Representation for Graph Data
Dongmian Zou, University of Minnesota, Twin Cities
##### Abstract:

Modern data are usually high-dimensional with noise and corruption. A useful representation of data has to be robust and address the data structure. In this talk, I will first present a class of robust models called the scattering transform that can be used to generated features from graph data. In graph scattering transforms, the representation is generated in an unsupervised manner based on graph wavelets. It is approximately invariant to permutations and stable to signal or graph manipulations. Numerical results show that it works effectively for classification and community detection problems. Next, I will address how the structure of data can be found using autoencoders. Indeed, in the framework of autoencoders, graph scattering transform can be applied to the important task of graph generation. It shows state-of-the-art performance in link prediction and can be used to generate molecular samples.

Tue Nov 19

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Tue Nov 19

## Topology Seminar

10:30am - Skybox
CORE @ Skybox - Skybox

##### Abstract:

https://www.fitmetrix.io/webportal/schedulemobile/f9719b20-4914-e911-a97...

Mon Nov 18

## Applied and Computational Math Colloquium

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

Mon Nov 18

## Student Number Theory Seminar

3:35pm - Vincent Hall 1
The Casselman-Shalika Formula for GL_2
Emily Tibor
##### Abstract:

This talk will focus on the Casselman-Shalika formula for GL_2 over a non-Archimedean local field, which is an explicit formula for the values of the spherical Whittaker function. A good amount of time will be dedicated to explaining the necessary background including Whittaker models and spherical vectors, which come together to form the spherical Whittaker function. We will then be ready to discuss the formula, Casselman's method of calculating it, and its significance.

Mon Nov 18

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Scalable Algorithms for Data-driven Inverse and Learning Problems
Tan Bui-Thanh, UT-Austin
##### Abstract:

Inverse problems and uncertainty quantification (UQ) are pervasive in scientific
discovery and decision-making for complex, natural, engineered, and societal systems.
They are perhaps the most popular mathematical approaches for enabling predictive scientific simulations that integrate observational/experimental data, simulations and/or
models. Unfortunately, inverse/UQ problems for practical complex systems possess these the simultaneous challenges: the large-scale forward problem challenge, the high dimensional parameter space challenge, and the big data challenge.

To address the first challenge, we have developed parallel high-order (hybridized) discontinuous Galerkin methods to discretize complex forward PDEs. To address the second challenge, we have developed various approaches from model reduction to advanced Markov chain Monte Carlo methods to effectively explore high dimensional parameter spaces to compute posterior statistics. To address the last challenge, we have developed a randomized misfit approach that uncovers the interplay between the Johnson-Lindenstrauss and the Morozov's discrepancy principle to significantly reduce the dimension of the data without compromising the quality of the inverse solutions.

In this talk we selectively present scalable and rigorous approaches to tackle these challenges for PDE-governed Bayesian inverse problems. Various numerical results for simple to complex PDEs will be presented to verify our algorithms and theoretical findings. If time permits, we will present our recent work on scientific machine learning for inverse and learning problems.

Mon Nov 18

## Topology Seminar

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

Mon Nov 18

## Topology Seminar

2:30pm - Ford Hall 110
Topology Seminar
TBA
Mon Nov 18

## Cockburn's Seminar

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

Fri Nov 15

## MCFAM Seminar

5:30pm - Vincent Hall 16
Data Science in the Life Insurance Industry
Gary Hatfield, Securian/University of Minnesota
##### Abstract:

Data Scientist has emerged as one of the hottest and most talked about jobs in the world today.  In my talk, I will provide an overview of how data science has emerged in the insurance industry. I will give some examples of how data science is being applied in life insurance and describe how the Actuarial profession is adapting. Bio: https://mcfam.dl.umn.edu/people/gary-hatfield

Fri Nov 15

## Combinatorics Seminar

3:30pm - Vincent Hall 570
Simplicial generation of Chow rings of matroids
Chris Eur, UC Berkeley
##### Abstract:

Matroids are combinatorial objects that capture the essence of linear independence. We first give a gentle introduction to the recent breakthrough in matroid theory, the Hodge theory of matroids, developed by Adiprasito, Huh, and Katz. By combining two prominent recent approaches to matroids, tropical geometric and Lie/Coxeter theoretic, we give a new presentation for the Chow ring of a matroid that further tightens the interaction between combinatorics and geometry of matroids. We discuss various applications, including a simplified proof of the main portion of the Hodge theory of matroids. This is joint work with Spencer Backman and Connor Simpson.

Fri Nov 15

## Probability Seminar

2:30pm - Vincent Hall 311
Joint seminar in math biology and probability: Mathematical Modelling in Immunotherapy of Melanoma
Anna Kraut, Bonn
##### Abstract:

Mathematical models can support biomedical research through identification of key mechanisms, validation of experiments, and simulation of new therapeutic approaches.

We investigate the evolution of melanomas under adoptive cell transfer therapy with cytotoxic T-cells. It was shown in experiments that phenotypic plasticity, more precisely an inflammation-induced, reversible dedifferentiation, is an important escape mechanism for the tumor. Recently, the effects of possible mutation to a permanently resistant genotype were studied by introducing knockout melanoma cells into the wildtype tumor.

We use a stochastic individual-based Markov process to describe the evolution of the tumor under various therapeutic approaches. It is an extension of the model introduced in the paper of Baar et al in 2016 and further includes the effects of T-cell exhaustion and some limited spatial component which results in additional non-linearities. The model is implemented as a hybrid algorithm that combines Gillespie-type stochastic calculations and a deterministic approximation to speed up simulations while keeping the effects of random events.

Numerical simulations confirm the resistance to therapy via phenotypic switching as well as genotypic mutation. T-cell exhaustion is identified as an important mechanism that is crucial in fitting the model to the experimental data. We gain further insights into how originally unfit knockout cells can accumulate under therapy, shield the wild type cells from the T-cells, and thus cause an earlier relapse. Going beyond the experiment, the possibility of naturally occurring rare mutations, in contrast to artificially introduced knockout cells, is explored in simulations and produces the same effects. Thus, the clinical relevance of the experimental findings can be confirmed.

Fri Nov 15

## Math Biology Seminar

2:30pm - Vincent Hall 311
Joint seminar in math biology and probability: Mathematical Modelling in Immunotherapy of Melanoma
Anna Kraut, Bonn
##### Abstract:

Mathematical models can support biomedical research through identification of key mechanisms, validation of experiments, and simulation of new therapeutic approaches.

We investigate the evolution of melanomas under adoptive cell transfer therapy with cytotoxic T-cells. It was shown in experiments that phenotypic plasticity, more precisely an inflammation-induced, reversible dedifferentiation, is an important escape mechanism for the tumor. Recently, the effects of possible mutation to a permanently resistant genotype were studied by introducing knockout melanoma cells into the wildtype tumor.

We use a stochastic individual-based Markov process to describe the evolution of the tumor under various therapeutic approaches. It is an extension of the model introduced in the paper of Baar et al in 2016 and further includes the effects of T-cell exhaustion and some limited spatial component which results in additional non-linearities. The model is implemented as a hybrid algorithm that combines Gillespie-type stochastic calculations and a deterministic approximation to speed up simulations while keeping the effects of random events.

Numerical simulations confirm the resistance to therapy via phenotypic switching as well as genotypic mutation. T-cell exhaustion is identified as an important mechanism that is crucial in fitting the model to the experimental data. We gain further insights into how originally unfit knockout cells can accumulate under therapy, shield the wild type cells from the T-cells, and thus cause an earlier relapse. Going beyond the experiment, the possibility of naturally occurring rare mutations, in contrast to artificially introduced knockout cells, is explored in simulations and produces the same effects. Thus, the clinical relevance of the experimental findings can be confirmed.

Fri Nov 15

## Dynamical Systems

2:30pm - Vincent Hall 20
The mathematics of taffy pulling
Jean-Luc Thiffeault, University of Wisconsin
##### Abstract:

Taffy is a type of candy made by repeated 'pulling' (stretching andfolding) a mass of heated sugar. The purpose of pulling is to get air
bubbles into the taffy, which gives it a nicer texture. Until the
late 19th century, taffy was pulled by hand, an arduous task. The
early 20th century saw an avalanche of new devices to mechanize the
process. These devices have fascinating connections to the
topological dynamics of surfaces, in particular with pseudo-Anosov
maps. Special algebraic integers such as the Golden ratio and the
lesser-known Silver ratio make an appearance, as well as more exotic
numbers. We examine different designs from a mathematical
perspective, and discuss their efficiency. This will be a "colloquium
style" talk that should be accessible to graduate students.

Fri Nov 15

## Reading Seminar on Automorphic Forms

1:30pm - Vincent Hall 1

Fri Nov 15

## Special Events and Seminars

1:25pm - Vincent Hall 213
"p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions
TBA
Fri Nov 15

## IMA/MCIM Industrial Problems Seminar

1:25pm - Lind 305
Pipelines, Graphs, and the Language of Shopping: Architecting Next Gen Machine Learning Capabilities for Retail
##### Abstract:

This talk will highlight the evolution of building out a data science capability in a retail environment as well as explore cutting-edge developments in constructing machine learning pipelines in the cloud, emerging advancements in time-series forecasting, applications of GPU accelerated graph processing for entity resolution, and how were adapting the latest research in language models to translate the language of shopping for the ultimate personalized experience

Thu Nov 14

## Student Combinatorics Seminar

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

Thu Nov 14

## Colloquium

3:35pm - Vincent Hall 16
$p$-adic estimates for exponential sums on curves
Joe Kramer-Miller, UC Irvine
##### Abstract:

A central problem in number theory is that of finding rational or integer solutions to systems of polynomials in several variables. This leads one naturally to the slightly easier problems of finding solutions modulo a prime $p$. Using a discrete analogue of the Fourier transformation, this modulo $p$ problem can be reformulated in terms of exponential sums. We will discuss $p$-adic properties of such exponential sums in the case of higher genus curves as well as connections to complex differential equations.

Thu Nov 14

## Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Commutative Algebra Seminar
Thu Nov 14

## Colloquium

2:30pm - Vincent Hall 16
Applications of Frobenius beyond prime characteristic.
Daniel Hernández, Univ. of Kansas
##### Abstract:

Abstract: Recall that the Frobenius morphism is simply the map sending an element in a ring of prime characteristic $p>0$ -- say, a polynomial with coefficients in a finite field -- to its $p$-th power. Though simple to define, Frobenius has proven to be a useful and effective tool in algebraic geometry, representation theory, number theory, and commutative algebra. Furthermore, and remarkably, some of the most interesting applications of Frobenius are to the study of objects defined over the complex numbers, and more generally, over a field of characteristic zero! In this talk, we will discuss some of these applications, with an eye towards classical singularity theory and birational algebraic geometry, both over the complex numbers.

Thu Nov 14

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Nov 13

## Student Number Theory Seminar

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

Wed Nov 13

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
Counting points and varieties and Malle's conjecture
Andy Odesky, University of Michigan
Wed Nov 13

## PDE Seminar

3:30pm - Vincent Hall 570
Serrin Lecture - Localization for the Anderson-Bernoulli model on the integer lattice
Charles Smart, University of Chicago
##### Abstract:

I will give a brief mathematical introduction to Anderson localization followed by a discussion of my recent work with Jian ding. In our work we establish localization near the edge for the Anderson Bernoulli model on the two dimensional lattice. Our proof follows the program of Bourgain--Kenig and uses a new unique continuation result inspired by Buhovsky--Logunov--Malinnikova--Sodin. I will also discuss recent work of by Li and Zhang on the three dimensional case.

Tue Nov 12

## Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Nov 12

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Nov 12

## Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Nov 12

## Colloquium

2:30pm - Vincent Hall 16
Unraveling Local Cohomology
Emily Witt, Univ. of Kansas
##### Abstract:

Local cohomology modules are fundamental tools in commutative algebra, due to the algebraic and geometric information they carry. For instance, they can help determine the number of equations necessary to define an affine variety. Unfortunately, however, the application of local cohomology is limited by the fact that these modules are typically very large (e.g., not finitely generated), and can be difficult to determine explicitly. In this talk, we discuss new techniques developed to understand the structure of local cohomology (e.g., coming from invariant theory). We also describe recently-discovered "connectedness properties" of spectra that local cohomology encodes.

Tue Nov 12

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Nov 12

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Latent Factor Models for Large-scale Data
Xiaoou Li, University of Minnesota, Twin Cities
##### Abstract:

Latent factor models are widely used to measure unobserved latent traits in social and behavioral sciences, including psychology, education, and marketing. Motivated by the applications of latent factor models to large-scale measurements which consist of many manifest variables (e.g. test items) and a large sample size, we study the properties of latent factor models under an asymptotic setting where both the number of manifest variables and the sample size grows to infinity. In this talk, I will introduce generalized latent factor models under exploratory and confirmatory settings. For the exploratory setting, we propose a constrained joint maximum likelihood approach for model estimation and investigate its theoretical properties. For the confirmatory setting, we study how the design information affects the identifiability and estimability of the model, and propose a rate-optimal estimator when the model is identifiable. The estimators can be efficiently computed through parallel computing. Our results provide insights on the design of large-scale measurement and have important implications on measurement validity.

Tue Nov 12

## Climate Seminar

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

## Applied and Computational Math Colloquium

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

Mon Nov 11

## Student Number Theory Seminar

3:35pm - Vincent Hall 1
Introduction to Rankin-Selberg Method
Shengmei An
##### Abstract:

Rankin-Selberg method has been one of the most powerful techniques for studying the Langlands program. In this talk, we will start with the original simplest example of the Rankin-Selberg method, and then come to a more general case of the Rankin-Selberg method on GL_m*GL_n where we can reduce the global integral to the more accessible lovely local integrals so that we can establish some of the important analytic properties of the L-functions.

Mon Nov 11

## Applied and Computational Mathematics Seminar

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

Mon Nov 11

## Topology Seminar

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

Mon Nov 11

## Topology Seminar

2:30pm - Ford Hall 110
Cochain models for the unit group of a differential graded algebra
Tyler Lawson, University of Minnesota
##### Abstract:

Abstract not available.

Mon Nov 11

## Cockburn's Seminar

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

Fri Nov 08

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Nov 08

## Combinatorics Seminar

3:30pm - Vincent Hall 570
Combinatorics via Deligne Categories
Chris Ryba, MIT
##### Abstract:

The Deligne category Rep(S_t) can be thought of as "interpolating" the representation categories of symmetric groups. After describing this category, I will explain how a calculation in the Deligne category can be used to prove stability properties of permutation patterns within conjugacy classes (joint with Christian Gaetz).

Fri Nov 08

## Probability Seminar

2:30pm - Vincent Hall 311
"Robust Synchronization via Cycle Consistency Inference
Yunpeng Shi, UMN
##### Abstract:

We propose a strategy for improving the existing methods for solving synchronization problems that arise from various computer vision tasks. Specifically, our strategy identifies severely corrupted relative measurements based on cycle consistency information. To the best of our knowledge, this paper provides the first exact recovery guarantees using cycle consistency information. This result holds for a noiseless but corrupted setting as long as the ratio of corrupted cycles per edge is sufficiently small. It further guarantees linear convergence to the desired solution. We also establish stability of the proposed algorithm to sub-Gaussian noise.

Fri Nov 08

## Math Biology Seminar

2:30pm - Vincent Hall 311
Joint seminar in math biology and probability: Mathematical Modelling in Immunotherapy of Melanoma
Anna Kraut, Bonn
##### Abstract:

Mathematical models can support biomedical research through identification of key mechanisms, validation of experiments, and simulation of new therapeutic approaches.

We investigate the evolution of melanomas under adoptive cell transfer therapy with cytotoxic T-cells. It was shown in experiments that phenotypic plasticity, more precisely an inflammation-induced, reversible dedifferentiation, is an important escape mechanism for the tumor. Recently, the effects of possible mutation to a permanently resistant genotype were studied by introducing knockout melanoma cells into the wildtype tumor.

We use a stochastic individual-based Markov process to describe the evolution of the tumor under various therapeutic approaches. It is an extension of the model introduced in the paper of Baar et al in 2016 and further includes the effects of T-cell exhaustion and some limited spatial component which results in additional non-linearities. The model is implemented as a hybrid algorithm that combines Gillespie-type stochastic calculations and a deterministic approximation to speed up simulations while keeping the effects of random events.

Numerical simulations confirm the resistance to therapy via phenotypic switching as well as genotypic mutation. T-cell exhaustion is identified as an important mechanism that is crucial in fitting the model to the experimental data. We gain further insights into how originally unfit knockout cells can accumulate under therapy, shield the wild type cells from the T-cells, and thus cause an earlier relapse. Going beyond the experiment, the possibility of naturally occurring rare mutations, in contrast to artificially introduced knockout cells, is explored in simulations and produces the same effects. Thus, the clinical relevance of the experimental findings can be confirmed.

Fri Nov 08

## Reading Seminar on Automorphic Forms

1:30pm - Vincent Hall 1

Fri Nov 08

## Special Events and Seminars

1:25pm - Vincent Hall 213
"p-Adic Cohomology, Exponential Sums, and Hypergeometric Functions
Steven Sperber
Thu Nov 07

## Student Combinatorics Seminar

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

Thu Nov 07

## Colloquium

3:35pm - Vincent Hall 16
Eisenstein Series on Loop Groups and their Metaplectic Covers
Manish Patnaik, University of Alberta
##### Abstract:

Both the Langlands-Shahidi method of studying automorphic L-functions and approach via the theory of Weyl group multiple Dirichlet series to studying moments of L-functions now require new classes of groups with which to work. In this talk, I will explain our progress on extending these techniques to certain infinite-dimensional Kac-Moody groups, namely loop groups (and their metaplectic covers). Of note in our work is the presence of two quite different types of Eisenstein series that exist on the same group and which need to be considered in conjunction with one other. This is a report on joint work in progress with H. Garland, S.D. Miller, and A. Puskas.

Thu Nov 07

## Commutative Algebra Seminar

2:30pm - Vincent Hall 209
The spectral sequence of a filtered complex
##### Abstract:

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

Thu Nov 07

## Colloquium

2:30pm - Vincent Hall 16
On various questions (and answers) in High-dimensional probability
Galyna Livshyts, Georgia Tech
##### Abstract:

In this talk, several topics from High-dimensional probability shall be discussed. This fascinating area is rich in beautiful problems, and several easy-to-state questions will be outlined. Further, some connections between them will be explained throughout the talk.

I shall discuss several directions of my research. One direction is invertibility properties of inhomogeneous random matrices: I will present sharp estimates on the small ball behavior of the smallest singular value of a very general ensemble of random matrices, and will briefly explain the new tools I developed in order to obtain these estimates.

Another direction is isoperimetric-type inequalities in high-dimensional probability. Such inequalities are intimately tied with concentration properties of probability measures. Among other results, I will present a refinement of the concavity properties of the standard gaussian measure in an n-dimensional euclidean space, under certain structural assumptions, such as symmetry. This result constitutes the best known to date estimate in the direction of the conjecture of Gardner and Zvavitch from 2007.

The above topics will occupy most of the time of the presentation. In addition, I shall briefly mention other directions of my research, including noise-sensitivity estimates for convex sets, or, in other words, upper bounds on perimeters of convex sets with respect to various classes of probability distributions. If time permits, I will discuss my other results, such as small ball estimates for random vectors with independent coordinates, and partial progress towards Levi-Hadwiger illumination conjecture for convex sets in high dimensions.

Thu Nov 07

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Nov 06

## Student Number Theory Seminar

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

Wed Nov 06

## PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Wed Nov 06

## Automorphic Forms and Number Theory

3:35pm - Vincent Hall 213
The automorphic heat kernel from a geometric perspective
Amy DeCelles, St. Thomas
Tue Nov 05

## Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Nov 05

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Nov 05

## Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Nov 05

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Nov 05

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Topics in Sparse Recovery via Constrained Optimization: Least Sparsity, Solution Uniqueness, and Constrained Exact Recovery
Seyedahmad Mousavi, University of Minnesota, Twin Cities
##### Abstract:

Sparse recovery finds numerous applications in different areas, for example, engineering, computer science, business, applied mathematics, and statistics. Sparse recovery is often formulated as relatively large-scale and challenging constrained (convex or nonconvex) optimization problems. Constraints are ubiquitous and important in many applications of sparse recovery, but they make analysis and computation nontrivial and require novel techniques to handle them. The goal of this talk is to present numerical and analytical techniques for constrained sparse recovery using convex analysis and optimization tools. Three topics are investigated in the realm of constrained sparse recovery.

First, we analyze quantitative adverse properties of different $p$-norm-based optimization problems with $p>1$, such as generalized basis pursuit, basis pursuit denoising, ridge regression, and elastic net. We show that their optimal solutions are least sparse for almost all measurement matrices and measurement vectors. Second, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. We apply these solution uniqueness results to a broad class of $\ell_1$-minimization problems in constrained sparse optimization, such as basis pursuit, LASSO, and polyhedral gauge recovery. Third, we propose a constrained matching pursuit algorithm for constrained sparse recovery and develop uniform conditions for exact support and vector recovery on constraint sets. The exact recovery via this algorithm not only depends on a measurement matrix but also critically relies on a constraint set. Hence, we identify an important class of constraint sets, called coordinate projection admissible. We then use the conic hull structure of these sets together with constrained optimization techniques to establish sufficient conditions for uniform exact recovery via this algorithm on coordinate projection admissible sets. These conditions are expressed in terms of the restricted isometry-like and the restricted orthogonality-like constants

Tue Nov 05

## Climate Seminar

11:15am - Vincent Hall 570
Climate Seminar
TBA
Mon Nov 04

## Applied and Computational Math Colloquium

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

Mon Nov 04

## Student Number Theory Seminar

3:35pm - Vincent Hall 1
Rankin-Selberg Method
May Shengmei
Mon Nov 04

## Applied and Computational Mathematics Seminar

3:35pm - Vincent Hall 6
Applied differential geometry and harmonic analysis in deep learning regularization
Wei Zhu, Duke University
##### Abstract:

Deep neural networks (DNNs) have revolutionized machine learning by gradually replacing the traditional model-based algorithms with data-driven methods. While DNNs have proved very successful when large training sets are available, they typically have two shortcomings: First, when the training data are scarce, DNNs tend to suffer from overfitting. Second, the generalization ability of overparameterized DNNs still remains a mystery.

In this talk, I will discuss two recent works to inject the modeling flavor back into deep learning to improve the generalization performance and interpretability of the DNN model. This is accomplished by DNN regularization through applied differential geometry and harmonic analysis. In the first part of the talk, I will explain how to improve the regularity of the DNN representation by enforcing a low-dimensionality constraint on the data-feature concatenation manifold. In the second part, I will discuss how to impose scale-equivariance in network representation by conducting joint convolutions across the space and the scaling group. The stability of the equivariant representation to nuisance input deformation is also proved under mild assumptions on the Fourier-Bessel norm of filter expansion coefficients.

Mon Nov 04

## Topology Seminar

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

Mon Nov 04

## Topology Seminar

2:30pm - Ford Hall 110
Topology Seminar
TBA
Mon Nov 04

## Cockburn's Seminar

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

Fri Nov 01

## MCFAM Seminar

5:30pm - Vincent Hall 16
Extrapolative Expectations, Financial Frictions, and Asset Prices
Yao Deng, University of Minnesota
##### Abstract:

I study how extrapolative expectations affect corporate real and financial activities and asset prices. Empirically, high misperception on earnings growth, a measure constructed to proxy for extrapolation, is associated with an increase in investment, debt issuance, equity issuance, and firm-level bond and stock prices in the short-term, but predicts a decline in all these activities and prices in the long-term. These patterns are more pronounced among small and financially constrained firms. Theoretically, I build a dynamic model with extrapolative expectations and financial frictions, and show that the interaction of these two frictions is crucial to explain the empirical findings. Intuitively, after a sequence of favorable shocks, agents extrapolate and become overoptimistic about future productivities. Firms invest and borrow more in the short-term. Lower perceived default probability improves financing conditions, further increasing investment and borrowing. Future realizations turn out worse than expected, making real and financial activities and asset prices subject to predictable reversals in the long-term.Bio: https://carlsonschool.umn.edu/faculty/yao-deng

Fri Nov 01

## Combinatorics Seminar

3:30pm - Vincent Hall 570
Combinatorics Seminar
Dongkwan Kim, UMN
##### Abstract:

For a Coxeter group W, a W-graph is a graph which produces a nice basis of the corresponding representation of W and also describes the action of W on the basis elements. Even when W is finite and its irreducible characters are known, W-graphs are still useful for understanding representations of W. In this talk, I will talk about W-graphs when W is an (extended) affine symmetric group, especially when these graphs are associated with two-row partitions. Also I will discuss the connection between them and Lusztigs periodic W-graph. This work is joint with Pavlo Pylyavskyy.

Fri Nov 01

## Probability Seminar

2:30pm - Vincent Hall 311
Probability Seminar

Fri Nov 01

## Reading Seminar on Automorphic Forms

1:30pm - Vincent Hall 1

Fri Nov 01

## Special Events and Seminars

1:25pm - Vincent Hall 213
p-Adic Banach Spaces and Completely Continuous Endomorphisms
Steven Sperber
Thu Oct 31

## Student Combinatorics Seminar

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

Thu Oct 31

## Colloquium

3:35pm - Vincent Hall 16
Differential operators on invariant rings
Anurag Singh, University of Utah
##### Abstract:

Work of Levasseur and Stafford describes the rings of differential operators on various classical invariant rings of characteristic zero; in each of these cases, the differential operators form a simple ring. Towards an attack on the simplicity of rings of differential operators on invariant rings of reductive groups over the complex numbers, Smith and Van den Bergh asked if reduction modulo p works for differential operators in this context. In joint work with Jack Jeffries, we establish that this is not the case for various classical groups.

Thu Oct 31

## Commutative Algebra Seminar

2:30pm - Vincent Hall 209
Spectral sequences
##### Abstract:

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

Thu Oct 31

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Wed Oct 30

## Student Number Theory Seminar

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

Wed Oct 30

## PDE Seminar

3:35pm - Vincent Hall 570
PDE Seminar

Wed Oct 30

## Automorphic Forms and Number Theory

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

Tue Oct 29

## Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Oct 29

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Oct 29

## Dynamical Systems

2:30pm - Vincent Hall 209
Dynamical Systems Seminar

Tue Oct 29

## Differential Geometry and Symplectic Topology Seminar

1:25pm - Vincent Hall 570
Differential Geometry and Sympletic Topology
TBA
Tue Oct 29

## IMA Data Science Lab Seminar

1:25pm - Lind 305
Highly Likely Clusterable Data With No Cluster
Mimi Boutin, Purdue University
##### Abstract:

Data generated as part of a real-life experiment is often quite organized. So much so that, in many cases, projecting the data onto a random line has a high probability of uncovering a clear division of the data into two well-separated groups. In other words, the data can be clustered with a high probability of success using a hyperplane whose normal vector direction is picked at random. We call such data `highly likely clusterable. The clusters obtained in this fashion often do not seem compatible with a cluster structure in the original space. In fact, the data in the original space may not contain any cluster at all. This talk is about this surprising phenomenon. We will discuss empirical ways to detect it as well as how to exploit it to cluster datasets, especially datasets consisting of a small number of points in a high-dimensional space. We will also present a possible mathematical model that would explain this observed phenomenon. This is joint work with Alden Bradford (Purdue Math), Sangchun Han (Purdue ECE, now at Google) and Tarun Yellamraju (Purdue ECE, now at Qualcomm).

Mireille (Mimi) Boutin graduated with a bachelors degree in Physics-Mathematics from the University of Montreal. She received the Ph.D. degree in Mathematics from the University of Minnesota under the direction of Peter J. Olver. She joined Purdue University after a post-doctorate with David Mumford, David Cooper, and Ben Kimia at Brown University, Rhode Island, followed by a post-doctorate with Stefan Muller at the Max Plank Institute for Mathematics in the Sciences in Leipzig, Germany. She is currently an Associate Professor in the School of Electrical and Computer Engineering, with a courtesy appointment in the Department of Mathematics. Her research is in the area of signal processing, machine learning, and applied mathematics. She is a three-time recipient of Purdues Seed for Success Award. She is also a recipient of the Eta Kappa Nu Outstanding Faculty Award, the Eta Kappa Nu Outstanding Teaching Award and the Wilfred Duke Hesselberth Award for Teaching Excellence.

Tue Oct 29

## Climate Seminar

11:15am - Vincent Hall 570
Convergence and Equilibrium for Stochastic Models of Ecological Disturbances
James Broda, Bowdoin College
Mon Oct 28

## Applied and Computational Math Colloquium

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

Mon Oct 28

## Student Number Theory Seminar

3:35pm - Vincent Hall 1
"Part 2: Representation Stability, Étale Cohomology and Combinatorics of Configuration Spaces over Finite Fields"
David DeMark
##### Abstract:

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

Mon Oct 28

## Applied and Computational Mathematics Seminar

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

Mon Oct 28

## Topology Seminar

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

Mon Oct 28

## Topology Seminar

2:30pm - Ford Hall 110
Compactifying the étale topos
Elden Elmanto, Harvard University
##### Abstract:

The speaker has long feared the technicalities and intricacies of equivariant stable homotopy theory. Fortunately, beginning with the work of Glasman, major simplification on the foundations of the subject has been made (cf. the work of Ayala-Mazel-Gee-Rozenblyum, Nikolaus-Scholze and the Barwick school). We offer another perspective (that the speaker has a chance of understanding) on equivariant stable homotopy theory, at least for the group C_2, via algebraic geometry. We view it as a way to remedy an infamous annoyance: the 2-étale cohomological dimension of the field of real numbers is infinite. We do this by identifying the genuine C_2-spectra with a category of motives based on Real algebraic geometry ala Scheiderer. This is joint work with Jay Shah.

Mon Oct 28

## Cockburn's Seminar

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

Fri Oct 25

## MCFAM Seminar

5:30pm - Vincent Hall 16
Mortgage Prepayment Behavior
Messan Edorh and Bo Li, US Bank

Mon Oct 21

## Applied and Computational Mathematics Seminar

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

Mon Oct 21

## Topology Seminar

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

Mon Oct 21

## Topology Seminar

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

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

Mon Oct 21

## Cockburn's Seminar

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

Fri Oct 18

## MCFAM Seminar

5:30pm - Vincent Hall 16
MCFAM Seminar

Fri Oct 18

## Combinatorics Seminar

3:30pm - Vincent Hall 570
Combinatorics Seminar

Fri Oct 18

## Probability Seminar

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

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

Fri Oct 18

## Reading Seminar on Automorphic Forms

1:30pm - Vincent Hall 1

Fri Oct 18

## Special Events and Seminars

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

## Student Combinatorics Seminar

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

Thu Oct 17

## Colloquium

3:35pm - Vincent Hall 16
Colloquium

Thu Oct 17

## Colloquium

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

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

Thu Oct 17

## Commutative Algebra Seminar

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

## Differential Geometry and Symplectic Topology Seminar

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

## Student Number Theory Seminar

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

Wed Oct 16

## PDE Seminar

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

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

Wed Oct 16

## Automorphic Forms and Number Theory

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

Tue Oct 15

## Special Events and Seminars

4:30pm - Vincent Hall 301
Arithmetic Geometry Seminar

Tue Oct 15

## Colloquium

3:30pm - Vincent Hall 16
Colloquium

Tue Oct 15

## Dynamical Systems

2:30pm - Vincent Hall 209
Forecasting U.S. elections with compartmental models of infection