Past Seminars

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). 

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).

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.

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.

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).

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

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.

Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Abstract:

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

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).

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.

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.

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-

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).

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.

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.

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.

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

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).

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.

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.

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

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.

Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

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).

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.

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

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.

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."

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

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.

Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

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).

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.

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

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.

Abstract:

We introduce a financial portfolio optimization framework that allows us to automatically select the relevant assets and estimate their weights by relying on a sorted l1-Norm penalization, henceforth SLOPE. To solve the optimization problem, we develop a new efficient algorithm, based on the Alternating Direction Method of Multipliers. SLOPE is able to group constituents with similar correlation properties, and with the same underlying risk factor exposures. Depending on the choice of the penalty sequence, our approach can span the entire set of optimal portfolios on the risk-diversification frontier, from minimum variance to the equally weighted. Our empirical analysis shows that SLOPE yields optimal portfolios with good out-of-sample risk and return performance properties, by reducing the overall turnover, through more stable asset weight estimates. Moreover, using the automatic grouping property of SLOPE, new portfolio strategies, such as sparse equally weighted portfolios, can be developed to exploit the data-driven detected similarities across assets.

Bio: Sandra Paterlini is full professor at the University of Trento, Italy. From 2013 to 2018, she held the Chair of Financial Econometrics and Asset Management at EBS Universität für Wirtschaft und Recht, Germany. Before joining EBS, she was assistant professor in statistics at the Faculty of Economics at the University of Modena and Reggio E., Italy. From 2008 to 2012, she has been a long-term visiting professor at the School of Mathematics, University of Minnesota. Her research on financial econometrics, statistics, operational research and machine learning have been predominantly interdisciplinary and often with an applied angle. Her work experience as a business consultant in finance and as a collaborator of central banks, such as for European Central Bank, Deutsche Bundesbank and the Fed Cleveland, has given her valuable input to guide and validate her research. Furthermore, she spent many years abroad (US, Germany, UK, and Denmark) to broaden and improve her skills further and to establish an international network of collaborators. She has been a consultant on business projects related to style analysis, portfolio optimization and risk management.

Her latest research interests are on machine learning methods for asset allocation, network analysis, risk management and ESG.

Abstract:

Many data in real-world applications lie in a high-dimensional space but are concentrated on or near a low-dimensional manifold. Our goal is to estimate functions on the manifold from finite samples of data. This talk focuses on an efficient approximation theory of deep ReLU networks for functions supported on low-dimensional manifolds. We construct a ReLU network for such function approximation where the size of the network grows exponentially with respect to the intrinsic dimension of the manifold. When the function is estimated from finite samples, we proved that the mean squared error for the function approximation converges as the training samples increases with a rate depending on the intrinsic dimension of the manifold instead of the ambient dimension of the space. These results demonstrate that deep neural networks are adaptive to low-dimensional geometric structures of data. This is a joint work with Minshuo Chen, Haoming Jiang, Tuo Zhao (Georgia Institute of Technology).

Dr. Wenjing Liao is an assistant professor in the School of Mathematics at Georgia Tech. She obtained her Ph.D. in mathematics at University of California, Davis in 2013. She was a visiting assistant professor at Duke University from 2013 to 2016, as well as a postdoctoral fellow at Statistical and Applied Mathematical Sciences Institute from 2013 to 2015. She worked at Johns Hopkins University as an assistant research scientist from 2016 to 2017. She works on theory and algorithms in the intersection of applied math, machine learning and signal processing. Her current research interests include multiscale methods for dimension reduction, statistical learning theory, and deep learning.

Abstract:

  In contrast to the traditional network paradigm, the dynamics of network social contagion processes are often mediated by interactions between multiple nodes. These interactions can profoundly modify the dynamics of contagion processes, resulting in bistability, hysteresis, and explosive transitions. We present a mean-field description of the dynamics of the SIS model on hypergraphs and use it to study the effect of heterogeneity on contagion dynamics. As an illustrative case, we focus on the example of a hypergraph where contagion is mediated by both links(pairwise interactions) and triangles (three-way interactions). We consider two different mechanisms of higher-order contagion and healing, and the cases where links and triangles connect preferentially to the same nodes or are chosen independently of each other. We find that explosive transitions can be suppressed by heterogeneity in the link degree distribution when links and triangles are chosen independently, or when link and triangle connections are positively correlated when compared to the uncorrelated case. In addition, we discuss the effect of assortative hypergraph structure on the contagion dynamics.

Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Abstract:

We present some modern problems in market risk modeling. Market risk regulations are in the process of changing at the Basel level. This represents new and active areas of R&D for Quants in the risk management space, particularly in banks, insurance companies and large buy-side institutions. The spectrum is broad, from highly theoretical aspects such as elicitiblity of expected shortfall, or invariance of FX risk capture, to highly applied areas such as the modeling of rarely observed variables.

Hany Farag is Senior Director and Head of Risk Methodology and Analytics at CIBC. Prior to his current position he was a partner at Eastmoor Capital Partners, LLP; Managing Director and Head of FX Statistical Arbitrage at CIBC; and Head of Quantitative Research at OANDA Corporation. Prior to his industry positions he was a Postdoctoral Fellow at Caltech and at Rice University. He holds a PhD in Mathematical Analysis from Yale, a MS in Theoretical Physics from Yale, and a BSC in Electronics and Communication Engineering from Ain Shams.

Abstract:

p-adic Hodge theory is one of the most powerful tools in modern arithmetic geometry. In this talk, I will review p-adic Hodge theory of algebraic varieties, present current developments in p-adic Hodge theory of analytic varieties, and discuss some of its applications to problems in number theory.

Abstract:

In this talk, I will explain how to construct the two-dimensional continuum random field Ising model via scaling limits of a random field perturbation of the critical two-dimensional Ising model with diminishing disorder strength. Almost surely with respect to the continuum random field given by a white noise, the law of the magnetisation field is singular with respect to that of the two-dimensional continuum pure Ising model constructed by Camia, Garban and Newman. Based on joint work with Adam Bowditch.

Abstract:

In many scientific areas, a deterministic model (e.g., a differential equation) is equipped with parameters. In practice, these parameters might be uncertain or noisy, and so an honest model should provide a statistical description of the quantity of interest. Underlying this computational question is a fundamental one - If two "similar" functions push-forward the same measure, are the new resulting measures close, and if so, in what sense? I will first show how the probability density function (PDF) can be approximated, using spectral and local methods, and present applications to nonlinear optics. We will then discuss the limitations of PDF approximation, and present an alternative Wasserstein-distance formulation of this problem, which yields a much simpler theory.

Amir Sagiv is a Chu Assistant Professor of Applied Mathematics at Columbia University. Before that, Amir completed his Ph.D. in Applied Mathematics at Tel Aviv University.

Abstract:

The Kuramoto model (KM) describes the evolution of phase oscillators

rotating with random frequencies and interacting with each other through

nonlinear coupling. The spatially extended model  also includes a graph describing

the connectivity of the network. In the thermodynamic limit, the KM is approximated

by the Vlasov equation, a hyperbolic PDE describing the evolution of the probability

distribution of the oscillators in the phase space.

I will review the linear stability analysis of mixing, a steady state solution of the

Vlasov equation and will relate the bifurcations of mixing to spatiotemporal patterns

observed in the KM right after mixing loses stability. These patterns include stationary

and travelling clusters, twisted states, chimera states, and combinations of the above.

In contrast to reaction-diffusion systems, where patterns are expressed by smooth

solutions, they are served by tempered distributions for the model at hand.

I will also discuss the extension of these results to the KM with inertia,

which is used for modeling dynamics of power grids. This talk is based on the  joint work with

Hayato Chiba (Tohoku University) and Matthew Mizuhara (The College of New Jersey).

Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Abstract:

Modern Machine Learning (ML) represents everything as vectors, from documents, to videos, to user behavior. This representation makes it possible to accurately search, retrieve, rank, and classify different items by similarity and relevance. Running real-time applications that rely on large numbers of such high dimensional vectors requires a dedicated data infrastructure called a Vector Database. In this talk we will discuss the need for such infrastructure, the algorithmic and engineering challenges in building a vector database, and open problems we still have no adequate solutions for. Time permits, I will introduce Pinecone, the first serverless vector database.

Edo is the Founder-CEO of Pinecone. Before Pinecone was a Director at AWS and the head of Amazon AI Labs and a Senior Director at Yahoo running the scalable Machine Learning Platforms group. He holds a PhD in Computer Science from Yale University and a B.Sc. in Physics and Computer Science from Tel Aviv University.  He was also a postdoctoral fellow in Applied Mathematics at Yale and an adjunct professor at Tel Aviv University. He is the author of more than 75 academic papers and patents on topics such as machine learning, systems, and optimization. 

Abstract:

Consider the optimization problem where we maximize the quadratic form of a large Gaussian matrix over the unit L_p ball. The case p = 2 corresponds to the top eigenvalue of the Gaussian Orthogonal Ensemble. On the other hand, when p = ?,the maximum value is the ground state energy of the mean-field Ising spin glass model and its limit can be expressed by the Parisi formula. In the talk, I will describe the limit of this optimization problem for general p and discuss some results on the behavior of optimizers along with some open problems.

This is joint work with Wei-Kuo Chen.

Abstract:

Mathematical models of biological systems are often validated by fitting to the average behavior in an often small experimental dataset. Here we ask the question of whether mathematical predictions for the average are actually applicable in samples that deviate from the average. We will explore this in the context of a mouse model of melanoma treated with two forms of immunotherapy: immune-modulating oncolytic viruses and dendritic cell injections. We will demonstrate how a mathematically optimal protocol for treating the average mouse can lack robustness, meaning the “best treatment for the average” can fail to be optimal (and in fact, can be far from optimal) in mice that differ from the average. We also show how mathematics can be used to identify an optimal treatment protocol that is robust to perturbations from the average. Time permitting, we will also explore how robustness influences the personalization of treatment protocols for individual mice.Zoom details:Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8

Abstract:

A very common phenomenon in biology and ecology isthe collective movement of individuals, whether thesebe birds, fish, cells, etc. This leads to the general question: Whatare the hallmarks of collective movement?In this talk, I will review an interdisciplinary study we have been carrying out over the past decade on a powerful model paradigm for collective cell migration, namely, the chick cranial neural crest. I will show how a relatively simple multiscale hybrid cellular automaton model, combined with experimental studies, can lead to new insights into the phenomenon of collective cell migration.Zoom details:Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8

Abstract:

Compartmental models for epidemiological modeling are a classic tool. In this talk I will share work we did to understand the effects of various testing strategies using a straightforward SIR model. I will also cover an extension to the typical SIR model to account for geographic heterogeneity and the incorporation of mobility data.

Natalie Sheils is a research scientist at UnitedHealth Group Research and Development. She earned her PhD in Applied Mathematics from the University of Washington in 2015 and then completed a postdoctoral fellowship at the University of Minnesota School of Mathematics. Her current research includes disease modeling and applications of healthcare data. She is involved in scientific policy and previously served on the SIAM Committee on Science Policy (2018-2019) and is now on the AMS Committee on Science Policy (2021-2024). 

Abstract:

Let X be a sparse generic matrix, i.e. a matrix whose entries are either zeros or distinct variables. A sparse determinantal variety is the locus where X does not have full rank. While determinantal varieties, i.e. degeneracy loci of matrices whose entries are distinct variables with no zeros, are in many respects well-understood, this is not yet the case for sparse determinantal varieties. However, sparse determinantal varieties have recently received increased attention, as new approaches for studying them have been introduced by Boocher (2011) and subsequently in a series of works by Conca, De Negri and myself (2015-2020). Blowup algebras - such as the Rees algebra, the special fiber ring, and the associated graded ring - are an active area of study within commutative algebra. They are algebraic objects related to the concept of blowing up a variety along a subvariety. In this talk, I will present some new results on the Rees algebra and the fiber ring of sparse determinantal varieties. Our approach makes an essential use of the theory of SAGBI bases, which I will introduce during the talk. The new results that I will present are part of a joint work with E. Celikbas, E. Dufresne, L. Fouli, K.-N. Lin, C. Polini, and I. Swanson, which was started during the collaborative conference WICA - Women in Commutative Algebra.See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Abstract:

Convolutional neural networks (CNNs) are the go-to tool for signal processing tasks in machine learning. But how and why do they work so well? Using the basic guiding principles of CNNs, namely their convolutional structure, invariance properties, and multi-scale nature, we will discuss how the CNN architecture arises as a natural bi-product of these principles using the language of nonlinear signal processing. In doing so we will extract some core ideas that allow us to apply these types of algorithms in various contexts, including the multi-reference alignment inverse problem, generative models for textures, and supervised machine learning for quantum many particle systems. Time permitting, we will also discuss how these core ideas can be used to generalize CNNs to manifolds and graphs, while still being able to provide mathematical guarantees on the nature of the representation provided by these tools. 

Matthew Hirn is an Associate Professor in the Department of Computational Mathematics, Science & Engineering and the Department of Mathematics at Michigan State University. At Michigan State he is the scientific leader of the ComplEx Data Analysis Research (CEDAR) team, which develops new tools in computational harmonic analysis, machine learning, and data science for the analysis of complex, high dimensional data. Hirn received his B.A. in Mathematics from Cornell University and his Ph.D. in Mathematics from the University of Maryland, College Park. Before arriving at MSU, he held postdoctoral appointments in the Applied Math Program at Yale University and in the Department of Computer Science at Ecole Normale Superieure, Paris. He is the recipient of the Alfred P. Sloan Fellowship (2016), the DARPA Young Faculty Award (2016), the DARPA Director’s Fellowship (2018), and the NSF CAREER award (2019), and was designated a Kavli Fellow by the National Academy of Sciences (2017).

Abstract:

I will describe my experience working in the area of algorithm development for implantable medical devices designed to improve heart failure patient management.  Signs and symptoms have been the hallmark of clinical assessment of heart failure (HF) patients. Current HF management takes a reactive approach, relying on patients recognizing symptoms and seeking help. However, patients often do not recognize their symptoms, resulting in late identification of a worsening condition which often results in hospitalization.  HeartLogic™ monitors patients’ HF status by assessing objective information from multiple physiological trends that are associated with common signs and symptoms of HF. HeartLogic fuses information from individual trends into a single diagnostic index and alerts clinicians when the patient’s condition changes in the worsening direction, enabling more timely ambulatory remote patient management.  HeartLogic is the first and only FDA approved Heart Failure Diagnostic in implantable cardiac therapy devices with remote alert capability. 

Julie is an R&D Director at Boston Scientific Corporation where she leads a team of scientists and engineers focused on developing diagnostic and therapy technology for improved cardiac patient management.  Julie joined Boston Scientific (previously Guidant Corporation) in 2001 after completing her PhD in electrical engineering at the University of Michigan.  She began her career as a research scientist focused on tachyarrhythmia algorithms, and subsequently transitioned to research management roles.  In 2005 Julie took on leadership of a team focused on developing diagnostic technology for heart failure monitoring.  She led this group through research and design of multiple diagnostic features that have been commercialized, including a novel multi-sensor diagnostic monitoring technology, HeartLogic™, proven to effectively detect early signs of worsening heart failure in patients indicated for an implantable cardiac rhythm management therapy device. 

Abstract:

We discuss the formation of singularities (shocks) for the compressible Euler equations with the ideal gas law. We provide a constructive proof of stable shock formation from smooth initial datum, of finite energy, and with no vacuum regions. Via modulated self-similar variables, the blow-up time and location can be explicitly computed, the geometry of the shock set can be understood, and at the blow-up time the solutions can be shown to have precisely Holder 1/3 regularity. Additionally, for the non-isentropic problem we show that sound waves interact with entropy waves to produce vorticity at the shock. This talk is based on joint work with Tristan Buckmaster and Steve Shkoller.

Abstract:

There are many natural sequences of moduli spaces in algebraic geometry whose homology approaches a "limit", despite the fact that the spaces themselves have growing dimension. If these moduli spaces are defined over a field K, this limiting homology carries an extra structure -- an action of the Galois group of K -- which is arithmetically interesting.

In joint work with Feng and Galatius, we compute this action (or rather a slight variant) in the case of the moduli space of abelian varieties. I will explain the answer and why I find it interesting. No familiarity with abelian varieties will be assumed -- I will emphasize topology over algebraic geometry.

Abstract:

Deep convolutional neural networks (CNN) have been developed and applied to data on Euclidean domains as well as non-Euclidean ones. In this talk, we introduce a framework of decomposing convolutional filters over a truncated set of basis filters, which applies to the standard CNN, group-equivariant CNN, as well as convolution on graphs. The basis decomposition reduces the model and computational complexity of deep CNNs with an automatically imposed filter regularity. First, for group equivariant CNNs, a joint basis decomposition over space and group geometry achieves group equivariance in image data, including rotation and scaling groups, with provable representation stability with respect to the geometric deformation of input data. Second, the decomposed convolution on graphs provides a unified framework for several graph convolution models. The graph convolution with low-rank local filters has enlarged expressiveness to represent graph signals than spectral graph convolutions, and shows empirical advantage on facial expression and action recognition datasets. At last, when allowing the light-weighted basis layer to be adapted to varying modals in data, the decomposition also provides a new way of invariant feature learning across domains, as well as conditional image generation. Joint work with Qiang Qiu, Ze Wang, Zichen Miao, Wei Zhu, Robert Calderbank, and Guillermo Sapiro.

Xiuyuan Cheng is an assistant professor of mathematics at Duke University. Dr. Cheng is interested in theoretical and computational problems in high-dimensional data analysis and machine learning, particularly on spectral methods, kernel matrices, and neural networks. Dr. Cheng's work is supported by NSF, NIH, and the Alfred P. Sloan Foundation.

Abstract:

What unites all of the things listed in this title? You'll have to show up to find out. This work is based on the concept of tradeoffs, a central idea in ecology and evolutionary biology. For example, the evolution of life history strategies is often framed in the language of tradeoffs. Behavioural ecologists may be interested in the tradeoffs inherent in the allocation of time (e.g., between foraging and vigilance) and resources (e.g., how much energy to invest in a reproductive attempt). Conservationists and wildlife managers must also consider tradeoffs between cost, political pressures, and management goals. Stochastic dynamic programming (SDP) is a powerful and flexible method for exploring optimal tradeoffs and has been used in a broad range of applications. In the last 30 years, concomitant with the development of SDP methods in ecology and evolution, matrix methods have emerged as another powerful tool for analyzing ecological systems. I will discuss how reformulating SDP problems in matrix notation allows us to propose a novel matrix method for solving SDP models, using intuition familiar to mathematical ecologists from matrix population models. Zoom details:Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8

Abstract:

We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building on a global–local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we model dependence between the local scale parameters. The resulting processes inherit the desirable shrinkage behaviour of popular global–local priors, such as the horseshoe prior, but provide additional localized adaptivity, which is important for modelling time series data or regression functions with local features. We construct a computationally efficient Gibbs sampling algorithm based on a Pólya–gamma scale mixture representation of the process proposed. Using dynamic shrinkage processes, we develop a Bayesian trend filtering model that produces more accurate estimates and tighter posterior credible intervals than do competing methods, and we apply the model for irregular curve fitting of minute?by?minute Twitter central processor unit usage data. In addition, we develop an adaptive time varying parameter regression model to assess the efficacy of the Fama–French five?factor asset pricing model with momentum added as a sixth factor. Our dynamic analysis of manufacturing and healthcare industry data shows that, with the exception of the market risk, no other risk factors are significant except for brief periods. If time permits, we will also highlight extensions to change point analysis and adaptive outlier detection. Bio: David S. Matteson is Associate Professor of Statistics and Data Science at Cornell University, where he is a member of the ILR School, Computing and Information Science, the Center for Applied Mathematics, the Field of Operations Research, and the Program in Financial Engineering, and teaches statistics, data science, and financial engineering courses. Professor Matteson received his PhD in Statistics at the University of Chicago (2008) and his BSB in Finance, Mathematics, and Statistics at the University of Minnesota (2003). He received a CAREER Award from the National Science Foundation. He is currently an Associate Editor of the Journal of the American Statistical Association-Theory and Methods, The American Statistician, and Statistica Sinica. He is an elected officer for the Business and Economic Statistics Section of the American Statistical Association. He is coauthor of `Statistics and Data Analysis for

Abstract:

In 1916, Ramanujan made a conjecture that can be stated in completely elementary terms: he predicted an upper bound on the coefficients of a power series obtained by expanding a certain infinite product. In this talk, I will discuss a more sophisticated interpretation of this conjecture, via the Fourier coefficients of a highly symmetric function known as a modular form. I will give a hint of the idea in Deligne's proof of the conjecture in the 1970's, who related it to the arithmetic geometry of smooth projective varieties over finite fields. Finally, I will discuss generalisations of this conjecture and some recent progress on these using the machinery of the Langlands program. The last part is based on joint work with Allen, Calegari, Gee, Helm, Le Hung, Newton, Scholze, Taylor, and Thorne.

Abstract:

The addition of an arbitrarily weak random field to low-dimensional classical statistical physics models leads to the "rounding" of first-order phase transitions at all temperatures, as predicted in 1975 by Imry and Ma and proved rigorously in 1989 by Aizenman and Wehr. This phenomenon was recently quantified for the two-dimensional random-field Ising model (RFIM), proving that it exhibits exponential decay of correlations at all temperatures. The RFIM analysis relies on monotonicity (FKG) properties which are absent in many other classical models. The talk will present new results on the quantitative aspects of the phenomenon for general systems with discrete and continuous symmetries, including Potts, spin O(n), spin glass and height function models.
Joint work with Paul Dario and Matan Harel.

Abstract:

Detecting differences and building classifiers between a family of distributions, given only finite samples, has had renewed interest due to data science applications in high dimensions.   Applications include survey response effects, topic modeling, and various measurements of cell or gene populations per person.  Recent advances have focused on kernel Maximum Mean Discrepancy and Optimal Transport.  However, when the family of distributions are concentrated near a low dimensional structure, or when the family of distributions being considered is generated from a family of simple group actions, these algorithms fail to exploit the reduced complexity.  In this talk, we'll discuss the theoretical and computational advancements that can be made under these assumptions, and their connections to harmonic analysis, approximation theory, and group actions. Similarly, we'll use both techniques to develop methods of provably identifying not just how much the distributions deviate, but where these differences are concentrated. We'll also focus on applications in medicine, generative modeling, and supervised learning.

Alex Cloninger is an Assistant Professor in Mathematics and the Hal?c?o?lu Data Science Institute at UC San Diego. He received his PhD in Applied Mathematics and Scientific Computation from the University of Maryland in 2014, and was then an NSF Postdoc and Gibbs Assistant Professor of Mathematics at Yale University until 2017, when he joined UCSD.   Alex researches problems in the area of geometric data analysis and applied harmonic analysis.  He focuses on approaches that model the data as being locally lower dimensional, including data concentrated near manifolds or subspaces.  These types of problems arise in a number of scientific disciplines, including imaging, medicine, and artificial intelligence, and the techniques developed relate to a number of machine learning and statistical algorithms, including deep learning, network analysis, and measuring distances between probability distributions.

Abstract:

The Euler equation describing motion of ideal fluid goes back to 1755. The analysis of the equation is challenging since it is nonlinear and nonlocal. Its solutions are often unstable and spontaneously generate small scales. The fundamental question of global regularity vs finite time singularity formation remains open for the Euler equation in three spatial dimensions. In this lecture, I will review the history of this question and its potential connection with the arguably greatest unsolved problem of classical physics, turbulence. Results on small scale and singularity formation in two dimensions and for a number of related models will also be presented.

Abstract:

The notochord, the defining feature of chordates, is essentially a soft cylinder patterned in early development by a small number of interior cells. Our analysis of packing patterns of vacuolated cells in zebrafish notochords reveals that the characteristic "staircase" pattern, or the alternate patterns observed in mutants, are governed by a simple and robust geometric measure. We have also noted that the notochord is weakly elliptical in cross section. From these observations, and from similar observations in a model gel system, we have identified a bidirectional interaction between cell packing pattern and the cross section of the surrounding tube. We model the mechanics of the notochord tube three ways, identifying a second key nondimensional ratio governing the pattern formation, and revealing previously unobserved packing patterns.  Zoom details:Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8

Abstract:

AttachedBio: Margie Rosenberg, PhD, FSA is the Assurant Health Professor of Actuarial Science Professor at the University of Wisconsin-Madison. Margie’s research interests are in the application of statistical methods to health care, and applying her actuarial expertise to cost and policy issues in health care. Her recent research involves linking social determinants to outcomes such as (i) assessing the impact of delayed attention to oral health issues on emergency department visits and (ii) assessing the impact of unhealthy behaviors on perceived health status and predicting individuals with persistent high expenditures. Prior to her starting on her academic career, Margie worked as a life actuary for Allstate Life Insurance Company in Northbrook, IL.Zoom Link: https://umn.zoom.us/j/99433158383?pwd=T3h6LzlTWCt4YW93Kzk3Rmg2bXQrZz09 

Abstract:

We present a novel active learning algorithm for community detection on networks. Our proposed algorithm uses a Maximal Expected Model Change (MEMC) criterion for querying network nodes label assignments. MEMC detects nodes that maximally change the community assignment likelihood model following a query. Our work is inspired by detection in the benchmark Stochastic Block Model (SBM), where we provide  sample complexity analysis and empirical study with SBM and real network data for binary as well as for multi-class settings. We also cover the most challenging case of sparse degree and below-detection-threshold SBMs, where we observe a super-linear error reduction. MEMC is shown to be superior to the random selection baseline and other state-of-the-art active learners.

Dan Kushnir is a distinguished member of technical staff at Bell Laboratories Data Science group where he has been since 2012. Before that he held the Gibbs assistant professor position at Yale University's Applied Math Program from 2008 to 2012. He obtained his PhD at the Weizmann Institute of Science on the subject of Multiscale Tools for Data Analysis in 2008. He hold BsC in Computer Science from the Hebrew University in Jerusalem. His Current Interests Include Active Learning, efficient Sampling, Harmonic Analysis, Numerical Analysis and Randomized methods.

Abstract:

We consider the problem of finding nearly optimal solutions of optimization problems with random objective functions. Two concrete problems we consider are (a) optimizing the Hamiltonian of a spherical or Ising p-spin glass model, and (b) finding a large independent set in a sparse Erdos-Renyi graph, both to be introduced in the talk. We consider the family of algorithms based on low-degree polynomials of the input. This is a general framework that captures methods such as approximate message passing and local algorithms on sparse graphs, among others. We show this class of algorithms cannot produce nearly optimal solutions with high probability. Our proof uses two ingredients. On the one hand both models exhibit the Overlap Gap Property (OGP) of near-optimal solutions. Specifically, for both models, every two solutions close to optimality are either close or far from each other. The second proof ingredient is the stability of the algorithms based on low-degree polynomials: a small perturbation of the input induces a small perturbation of the output. By an interpolation argument, such a stable algorithm cannot overcome the OGP barrier thus leading to the inapproximability. The stability property is established using concepts from Gaussian and Boolean Fourier analysis, including noise sensitivity, hypercontractivity, and total influence.

Joint work with Aukosh Jagannath and Alex Wein.

Abstract:

The concentration of measure phenomenon is an indispensable tool in the study of high-dimensional phenomena.
Nonetheless, there exist several key situations that yields suboptimal results. We will discuss how this probabilistic principle admits stronger forms in the presence of convexity and how the local version of them can be combined with a blend of analytic, combinatorial, and topological methods in order to obtain sharp small ball probabilities for norms in high dimensions. Time permitting we will present applications in asymptotic geometric analysis. Based on joint work with Grigoris Paouris and Konstantin Tikhomirov.

Abstract:

Mean-field games (MFG) is a framework to model and analyze huge populations of interacting agents that play non-cooperative differential games with applications in crowd motion, economics, finance, etc. Additionally, the PDE that arise in MFG have a rich mathematical structure and include those that appear in optimal transportation and density flow problems. In this talk, I will discuss applications of machine-learning techniques to solve high-dimensional MFG systems. I will present Lagrangian, GAN-type, and kernel-based methods for suitable types of MFG systems.

I am currently an Assistant Adjunct Professor at the Department of Mathematics at UCLA. I previously held postdoctoral and visiting positions at McGill University, King Abdullah University of Science and Technology, National Academy of Sciences of Armenia, and the Technical University of Lisbon. I have also been a Senior Fellow at the Institute for Pure and Applied Mathematics (IPAM) at UCLA for its Spring 2020 Program on High Dimensional Hamilton-Jacobi PDEs and a Simons CRM Scholar at the University of Montreal for its Spring 2019 Program on Data Assimilation: Theory, Algorithms, and Applications.

Abstract:

Local cohomology modules are (typically) very large algebraic objects that encode rich geometric information about the structure of a commutative ring. These modules are rarely finitely generated, but when the underlying space is smooth, there is often additional structure available that can lead to remarkable finiteness properties. For example, there are large classes of regular rings whose local cohomology is known to always have a finite set of associated primes. This property can fail over a complete intersection rings, but independent results of Hochster and Núñez-Betancourt (2017) or Katzman and Zhang (2017) have shown that at least in characteristic p > 0, the local cohomology of a hypersurface ring will still have closed support in the Zariski topology. It remains an open question whether this property holds in arbitrary codimension. In this talk, I will present my results on the local cohomology of a parameter ideal illustrating an obstruction to straightforwardly generalizing existing hypersurface strategies. I will then present joint work with Eric Canton on an alternative route of attack in higher codimension, involving a novel Frobenius-compatible simplicial complex of local cohomology modules.  See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Abstract:

We exhibit a large family of new, non-trivial stationary states of analytic regularity, that are arbitrarily close to the Kolmogorov flow on the square torus. Our construction of these stationary states builds on a degeneracy in the global structure of the Kolmogorov flow. This is in contrast with both the Kolmogorov flow on a rectangular torus and the Poiseuille flow in a channel, for which we can show that the only stationary states near them must be shears. This has surprising consequences in the context of inviscid damping in 2D Euler and enhanced dissipation in Navier-Stokes.Join Zoom Meetinghttps://umn.zoom.us/j/91765959125?pwd=RjRkSW9PNi9HNzVOb2lwb0tkWVVoZz09Meeting ID: 917 6595 9125Passcode: VinH16

Abstract:

This talk discusses multiple methods for clustering high-dimensional data, and explores the delicate balance between utilizing data density and data geometry. I will first present path-based spectral clustering, a novel approach which combines a density-based metric with graph-based clustering. This density-based path metric allows for fast algorithms and strong theoretical guarantees when clusters concentrate around low-dimensional sets. However, the method suffers from a loss of geometric information, information which is preserved by simple linear dimension reduction methods such as classic multidimensional scaling (CMDS). The second part of the talk will explore when CMDS followed by a simple clustering algorithm can exactly recover all cluster labels with high probability. However, scaling conditions become increasingly restrictive as the ambient dimension increases, and the method will fail for irregularly shaped clusters. Finally, I will discuss how a more general family of path metrics, combined with MDS, give low-dimensional embeddings which respect both data density and data geometry. This new method exhibits promising performance on single cell RNA sequence data and can be computed efficiently by restriction to a sparse graph.

Anna Little received her PhD from Duke University in 2011, where she worked under Mauro Maggioni to develop a new multiscale method for estimating the intrinsic dimension of a data set. From 2012-2017 she was an Assistant Professor of Mathematics at Jacksonville University, a primarily undergraduate liberal arts institution where in addition to teaching and research she served as a statistical consultant. In 2018 she began a research postdoc in the Department of Computational Mathematics, Science, and Engineering at Michigan State University, where she worked with Yuying Xie and Matthew Hirn on statistical and geometric analysis of high-dimensional data. She recently accepted a tenure-track position in the Department of Mathematics at the University of Utah, which will begin in January 2021.

Abstract:

To any poset on [n] we can associate a cone in a natural way. This is done by a correspondence between i < j and the half-space x_i <= x_j. To any cone (or fan of cones) we have a toric variety. We consider translations back and forth between properties of posets and toric varieties. From this point of view we can establish Oda's strong factorization conjecture in the special case of fans arising from posets. We will also preview in progress work joint with Josh Hallam on crepant resolutions and the Gorenstein property for toric varieties associated to posets.

Abstract:

Image compression, as a subset of image processing, intersects many areas of applied mathematics. In this talk, I will describe and compare the "classic" view of image compression, such as the JPEG algorithm and it's variants, against the "new kid on the block", namely compression using neural networks (NN). I will survey the relative merits of NN-based compression algorithms, provide a run-down of the inner workings, and discuss some of their flaws. We'll see that the neural network approach promises impressive performance gains over traditional image compression algorithms, though some hurdles still remain.

Chris Finlay is a research scientist at Deep Render, a UK startup focused on AI-based image and video compression. His background is in applied mathematics, but has spent time dabbling in machine leaning and computer science. Prior to moving to industry, he worked as a post-doc in machine learning, mainly researching neural ODEs, generative modeling, and the robustness of deep learning computer vision algorithms. He obtained a PhD in applied mathematics from McGill University, where he studied numerical methods for nonlinear elliptic PDEs.

Abstract:

The Langlands correspondence for complex curves is traditionally formulated in terms of sheaves rather than functions. Recently, Robert Langlands asked whether it is possible to construct a function-theoretic version. Together with Pavel Etingof and David Kazhdan, we have formulated a function-theoretic version as a spectral problem for (a self-adjoint extension of) an algebra of commuting differential operators on the moduli space of G-bundles of a complex algebraic curve.

I will start the talk with a brief introduction to the Langlands correspondence. I will discuss both the geometric and the function-theoretic versions for complex curves, and the relations between them. I will then present some of the results and conjectures from my joint work with Etingof and Kazhdan.

Abstract:

We derive a continuum mean-curvature flow as a scaling limit of a class of zero-range + Glauber interacting particle systems. The zero-range part moves particles while preserving particle numbers, and the Glauber part allows birth and death of particles, while favoring two levels of particle density. When the two parts are simultaneously seen in certain (different) time-scales, and the Glauber part is `bi-stable', a mean-curvature interface flow, incorporating a homogenized `surface tension' reflecting microscopic rates, between the two levels of particle density, can be captured as a limit of the mass empirical density. This is work with Perla El Kettani, Tadahisa Funaki, Danielle Hilhorst, and Hyunjoon Park.

Abstract:

This presentation will provide a current and in depth review of the Covid-19 pandemic. It will also provide a glimpse into the future as to how this pandemic will continue to unfold and the impact it will have worldwide.

Dr. Osterholm is Regents Professor, McKnight Presidential Endowed Chair in Public Health, the director of the Center for Infectious Disease Research and Policy (CIDRAP), Distinguished Teaching Professor in the Division of Environmental Health Sciences, School of Public Health, a professor in the Technological Leadership Institute, College of Science and Engineering, and an adjunct professor in the Medical School, all at the University of Minnesota. From June 2018 through May 2019, he served as a Science Envoy for Health Security on behalf of the US Department of State. He is also on the Board of Regents at Luther College in Decorah, Iowa.

Abstract:

In this talk, I consider the stability of traveling fronts connecting an invading state to an unstable ground state in a Ginzburg-Landau equation with an additional conservation law. This system appears generically as an amplitude equation for Turing pattern forming systems admitting a conservation law structure such as the Bénard-Marangoni convection problem. The main result is the nonlinear stability of sufficiently fast fronts with respect to perturbations which are exponentially localized ahead of the front. The proof is based on the use of exponential weights ahead of the front to stabilize the ground state. After presenting the general strategy, I discuss the specific challenges faced in the proof, namely the lack of a comparison principle and the fact that the invading state is only diffusively stable, i.e. perturbations of the invading state decay polynomially in time.

Zoom Link: https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Abstract:

Viruses encapsulate their genetic material into protein containers that act akin to molecular Trojan horses, protecting viral genomes between rounds of infection and facilitating their release into the host cell environment. In the majority of viruses, including major human pathogens, these containers have icosahedral symmetry. Mathematical techniques from group, graph and tiling theory can therefore be used to better understand how viruses form, evolve and infect their hosts, and point the way to novel antiviral solutions. In this talk, I will present a theory of virus architecture, that contains the seminal Caspar Klug theory as a special case and solves long-standing open problems in structural virology. I will also introduce mathematical models of symmetry breaking in viral capsids and discuss their consequences for our understanding of more complex viral geometries. By combining these geometric insights with a range of different mathematical and computational modelling techniques, I will demonstrate how viral life cycles can be better understood through the lens of viral geometry, and how such insights can act as drivers of discovery of novel anti-viral solutions. Join Zoom Meeting https://umn.zoom.us/j/94817303643?pwd=aHBrNFpzaFdLSU9HUjJybllla3M3QT09 Meeting ID: 948 1730 3643 Passcode: R90eZ8

Abstract:

 Modeling implied volatility surface (IVS) is of paramount importance to price and hedge an option. We contribute to the literature by modeling the entire IVS using recurrent neural network architectures, namely Convolutional Long Short Term Memory Neural Network (ConvLSTM) to produce multivariate and multi-step forecasts of the S&P 500 implied volatility surface. Using the daily S&P 500 index options from 2002 to 2019, we benchmark the ConvLSTM model against traditional multivariate time series VAR model, VEC model, and LSTM neural network. We find that both LSTM and ConvLSTM can fit the training data extremely well with mean absolute percentage error (MAPE) being 3.56%  and 3.88%, respectively. As for out-of-sample data, the ConvLSTM (8.26% ) model significantly outperforms traditional time series models as well as the LSTM model for a 1-day, 30-day, and 90-day horizon, for all moneyness groups and contract months of both calls and puts.  Zoom Link: https://umn.zoom.us/j/99433158383?pwd=T3h6LzlTWCt4YW93Kzk3Rmg2bXQrZz09  

Abstract:

Quantitative systems pharmacology (QSP) models are increasingly being used for decision making in the biotechnology/pharmaceutical (biopharma) industry. QSP models are typically systems of ordinary differential equations with some mechanistic level of detail of the disease and a therapy. Parameters in a QSP model may be estimated from data, or obtained from the literature or from input from disease/biology experts. Once parameter values or distributions are determined, a QSP model can be used for predictive purposes. I will show some examples of QSP models used in projects for various applications in the biopharma industry. I will also mention some of the issues and open problems for the use of QSP models. 

Dr. Moore is a mathematician who spent 11 years in academia working in modeling and optimization, primarily in oncology, immunology, and virology. While in academia, she won two teaching awards and received a National Science Foundation grant for her research. During 14 years in the biopharma industry, she has worked in a variety of therapeutic areas and drug development stages at Genentech, Certara, Bristol-Myers Squibb, AstraZeneca, and now Applied BioMath. In 2018, she was named a Fellow of the Society for Industrial and Applied Mathematics. Her current work includes mechanistic ODE systems modeling, modeling of tumor dynamics, optimization of combination regimens, and quantitative evaluation of predictive mathematical models. She graduated from the University of North Carolina at Chapel Hill in 1989, and earned her PhD in mathematics from Stony Brook University in New York in 1995.

Abstract:

In geometric measure theory there is interest in understanding measures by studying interactions with particular collections of sets. Here, we will discuss a recent characterization of Radon measures on R^n which are carried by the collection of m-Lipschitz graphs. That is, we will provide necessary and sufficient conditions for a Radon measure under which there exist countably many Lipschitz graphs that capture almost all of the mass. Our characterization will involve only countably many evaluations of the measure. This is joint work with Matthew Badger.Join Zoom Meetinghttps://umn.zoom.us/j/91765959125?pwd=RjRkSW9PNi9HNzVOb2lwb0tkWVVoZz09Meeting ID: 917 6595 9125Passcode: VinH16  

Abstract:

I will address some recent developments in geometric methods for optimization, statistics, and sampling. Within three specific examples, I will demonstrate how one can leverage geometric structure to achieve: 1) robust recovery results for nonconvex estimators, 2) fast statistical rates in Wasserstein barycenter estimation, and 3) efficient sampling algorithms. First, in regard to robust recovery, I consider the problems of robust subspace recovery and robust synchronization. Each of these problems has an underlying manifold structure that is exploited to yield state-of-the-art robustness guarantees and efficient algorithms. Next, I will discuss the problem of statistical estimation of Wasserstein barycenters and develop a condition that ensures fast rates for an efficiently computable estimator. Finally, I will show how the leveraging the structure of gradient flows on Wasserstein space allows one to develop fast rates of convergence for sampling algorithms. The discretization of these flows leads to novel sampling algorithms that offer distinct advantages over existing methods.

Tyler received his Ph.D. in Mathematics and M.S. in Statistics from the University of Minnesota in 2018, where he worked with Prof. Gilad Lerman on the problem of robust subspace recovery. Since then, he has been an Instructor in Applied Mathematics at MIT, where he has worked with Prof. Philippe Rigollet on problems related to optimization, optimal transport, and sampling.

Abstract:

 Climate Change is one of the most significant and yet poorly understood risks faced by organizations today. While there is general consensus on the climate impact of continued greenhouse gas emissions, there remains significant uncertainty in the exact timing and severity of most serious extreme events. This uncertainty has led to a 'tragedy of the horizons' among much of the financial sector, where short term risks and financial decisions need to be balanced against long term secular risks introduced by climate change. The risks posed by climate change can be broadly classified into two categories, physical and transition risks. Physical risks refer to the increased direct exposure to changing frequency and severity of extreme events. Transition risks pertain to impacts on traditional business models and sectors as society shifts towards a lower carbon economy. A comprehensive analysis for these risks necessarily involves rigorous portfolio stress testing and scenario analysis on both the asset and liability side of the balance sheet. While climate change is a global phenomenon, the specific weather extremes are very local. The embedded correlations and non-linear impacts  make financial outcome distributions skewed and fat tailed. The financial models used to assess climate change risk need to adequately reflect the complex spatio-temporal interactions between nature and physical/financial assets. The insurance industry, in its key role as a risk transfer intermediary is often at the forefront of the financial impacts of climate change. The industry is not a novice to dealing with climate risks emanating from extreme events, such as hurricanes, floods, wildfires, etc. In response to the significant earnings and capital impacts of such extreme events, the industry has evolved over the past 3 decades, a fairly robust toolkit to assess physical climate risks using sophisticated catastrophe risk models. We will discuss how these models can help assess physical climate risks in insurance portfolios and how a similar approach might be adapted for broader finance portfolios.  Bio: Dr. Manghnani is a senior risk and analytics executive at the PIMCO with a focus on the Insurance Linked Security asset class. He is also the Chief Actuary and Chief Risk Officer at Newport Re. Most recently, he was the Head of Catastrophe Risk Management and Analytics COE at AIG. In this role, he was responsible for implementing state of the art

Abstract:

  In this talk, I will present two works related to boundary layers in thefluid. The first result concerns the 2D Navier-Stokes equations linearized around the Couette flow in the periodic channel in the vanishing viscosity limit. We split the vorticity evolution into thefree-evolution (without a boundary) and a boundary corrector that is exponentially localized. If the initial vorticity perturbation is supported away from the boundary, we show inviscid damping of both thevelocity and the boundary layer's vorticity. We also observe that both velocity and vorticity satisfy the expected enhanced dissipation. This is joint work with Jacob Bedrossian. The second work is related to aboundary layer model designed to understand the Hou-Luo Scenario associated with the 3D Euler equation's blow-up. We show that there exists initial data which yields blow-up in the model. This is joint workwith Alexander Kiselev.Join Zoom Meetinghttps://umn.zoom.us/j/91765959125?pwd=RjRkSW9PNi9HNzVOb2lwb0tkWVVoZz09Meeting ID: 917 6595 9125Passcode: VinH16

Abstract:

We focus on developing a novel scalable graph-based semi-supervised learning (SSL) method for a small number of labeled data and a large amount of unlabeled data. Due to the lack of labeled data and the availability of large-scale unlabeled data, existing SSL methods usually encounter either suboptimal performance because of an improper graph or the high computational complexity of the large-scale optimization problem. In this paper, we propose to address both challenging problems by constructing a proper graph for graph-based SSL methods. Different from existing approaches, we simultaneously learn a small set of vertexes to characterize the high-dense regions of the input data and a graph to depict the relationships among these vertexes. A novel approach is then proposed to construct the graph of the input data from the learned graph of a small number of vertexes with some preferred properties. Without explicitly calculating the constructed graph of inputs, two transductive graph-based SSL approaches are presented with the computational complexity in linear with the number of input data. Extensive experiments on synthetic data and real datasets of varied sizes demonstrate that the proposed method is not only scalable for large-scale data, but also achieve good classification performance, especially for extremely small number of labels.

Dr. Li Wang is currently an assistant professor with Department of Mathematics and Department of Computer Science Engineering, University of Texas at Arlington, Texas, USA. She worked as a research assistant professor with Department of Mathematics, Statistics, and Computer Science at University of Illinois at Chicago, Chicago, USA from 2015 to 2017. She worked as the Postdoctoral Fellow at University of Victoria, BC, Canada in 2015 and Brown University, USA, in 2014. She received her Ph.D. degree in Department of Mathematics at University of California, San Diego, USA, in 2014. Her research interests include data science, large-scale optimization and machine learning.

Abstract:

For an organization with billions of dollars in assets, precise risk management is necessary to safeguard those assets. However, when the risks these assets are exposed to depend on the future performance of equities in complex ways, directly estimating them in real-time to the necessary precision can be prohibitively expensive. This talk discusses some approaches to resolving this tension via metamodeling techniques.Bio: Liban Mohamed is a final-year PhD student in the UW-Madison Department of Mathematics. His research focuses on the scattering theory of solutions to the Schrodinger equation on discrete spaces. The content of this talk is the result of a project hosted by the 2020 IMA Math-to-Industry Boot Camp with industry partners at Securian Financial.Zoom Link: https://umn.zoom.us/j/99433158383?pwd=T3h6LzlTWCt4YW93Kzk3Rmg2bXQrZz09     

Abstract:

Working at a national laboratory can be somewhere in between academia and industry. I will describe my perspective of what makes working at a lab unique, based on my experience in the Computing Research Center at Sandia National Laboratories. I will mention skills that will help a researcher succeed in this environment, many just those that will help anywhere. The constraints and priorities of national-security problems often give even abstracted problems unusual twists. I will summarize some example research projects from data science (streaming data management for cybersecurity, cooperative computing among autonomous data centers for counterterrorism) to solvers (highly parallel branch and bound) to the intersection of government and industry (e.g. sensor placement for municipal water networks with the US EPA).

Cynthia Phillips is a senior scientist at Sandia National Laboratories.  In her 30 years at the lab she has conducted research in combinatorial optimization, algorithm design and analysis, and parallel computation with more recent work in data science such as streaming algorithms. The applications reflect some of the diversity of Sandia's mission including scheduling, network and infrastructure surety, computational biology, computer security, quantum computing, neuromorphic computing, hardware/algorithm co-design, social network analysis, wireless networks and sensor placement (e.g. for municipal water networks for the EPA). Her work spans highly theoretical papers to general-purpose codes to applications. She has done extensive professional service including being a professional society officer and a conference chair. She is an Association for Computing Machinery distinguished scientist and a Society for Industrial and Applied Mathematics fellow. She received a B.A. in applied mathematics from Harvard University and a PhD in computer science from MIT.

Abstract:

 In this talk, I will describe a recent series of work with I.-J. Jeong on the incompressible Hall MHD equation without resistivity. This PDE, first investigated by the applied mathematician M. J. Lighthill, is a one-fluid description of magnetized plasmas with a quadratic second-order correction term (Hall current term), which takes into account the motion of electrons relative to positive ions. Curiously, we demonstrate the ill(!)posedness of the Cauchy problem near the trivial solution, despite the apparent linear stability and conservation of energy. Our ill posedness mechanism is sharp, in that it remains true under fractional dissipation of any subcritical order. On the other hand, we identify several regimes in which the Cauchy problem is well-posed, which not only includes the original setting that M. J. Lighthill investigated (namely, for initial data close to a uniform magnetic field) but also possibly large perturbations thereof. Central to our proofs is the viewpoint that the Hall current term imparts the magnetic field equation with a quasilinear dispersive character. With such a viewpoint, the key ill- and well-posedness mechanisms can be understood in terms of the properties of the bi-characteristic flow associated with the appropriate principal symbol.Join Zoom Meetinghttps://umn.zoom.us/j/91765959125?pwd=RjRkSW9PNi9HNzVOb2lwb0tkWVVoZz09Meeting ID: 917 6595 9125Passcode: VinH16  

Abstract:

We address two important subproblems of Structure from Motion Problem. The first subproblem is known as Multi-way Matching, where the input includes multiple sets, with the same number of objects and noisy measurements of fixed one-to-one correspondence maps between the objects of each pair of sets. Given only noisy measurements of the mutual correspondences, the Multi-way Matching problem asks to recover the correspondence maps between pairs of them. The desired output includes the original fixed correspondence maps between all pairs of sets. The second subproblem is called Multi-Perspective Simultaneous Embedding (MPSE). The input for MPSE assumes a set of pairwise distance matrices defined on the same set of objects and possibly along with the same number of projection operators. MPSE embeds points in 3D so that the pairwise distances are preserved under the corresponding projections. Our proposed algorithm for Multi-way Matching problem iteratively solves the associated non-convex optimization problem. We prove that for a specific noise model, if the initial point of our proposed iterative algorithm is good enough, the algorithm linearly converges to the unique solution. Numerical experiments demonstrate that our method is much faster and more accurate than the state-of-the-art methods. For MPSE, we propose a heuristic algorithm and provide an extensive quantitative evaluation with datasets of different sizes, as well as several examples that illustrate the quality of the resulting solutions.

I received my PhD in mathematics from the University of Minnesota in 2018, under the supervision of my advisor Prof. Gilad Lerman. Since 2018, I've been working as a Postdoctoral Research Associate at the Department of Mathematics of the University of Arizona.

Abstract:

Let $\alpha=(a,b,\ldots)$ be a composition. Consider the associated poset $F(\alpha)$, called a fence, whose covering relations are $$x_1\lhd x_2 \lhd \ldots\lhd x_{a+1}\rhd x_{a+2}\rhd \ldots\rhd x_{a+b+1}\lhd x_{a+b+2}\lhd \ldots\.$$ We study the associated distributive lattice $L(\alpha)$ consisting of all lower order ideals of $F(\alpha)$. These lattices are important in the theory of cluster algebras and their rank generating functions can be used to define $q$-analogues of rational numbers. In particular, we make progress on a recent conjecture of Morier-Genoud and Ovsienko that $L(\alpha)$ is rank unimodal. We show that if one of the parts of $\alpha$ is greater than the sum of the others, then the conjecture is true. We conjecture that $L(\alpha)$ enjoys the stronger properties of having a nested chain decomposition and having a rank sequence which is either top or bottom interlacing, the latter being a recently defined property of sequences. We verify that these properties hold for compositions with at most three parts and for what we call $d$-divided posets, generalizing work of Claussen and simplifying a construction of Gansner. This is joint work with Thomas McConville and Clifford Smyth.See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Abstract:

I will discuss several applications of random walks to graph-based learning, both for theoretical analysis and algorithm development. Graph-based learning is a field within machine learning that uses similarities between datapoints to create efficient representations of high-dimensional data for tasks like semi-supervised classification, clustering and dimension reduction. Our first application will be to use the random walk interpretation of the graph Laplacian to characterize the lowest label rate at which Laplacian regularized semi-supervised learning is well-posed. Second, we will show how analysis via random walks leads to a new algorithm that we call Poisson learning for semi-supervised learning at very low label rates. Finally, we will show how stochastic coupling of random walks can be used to prove Lipschitz estimates for graph Laplacian eigenfunctions on random geometric graphs, leading to new spectral convergence results.

This talk will cover joint work with many people, including Brendan Cook (UMN), Nicolas-Garcia Trillos (Wisconsin-Madison), Marta Lewicka (Pittsburgh), Dejan Slepcev (CMU), Matthew Thorpe (University Manchester).

Abstract:

In this talk, we will discuss a mathematical treatment of a disordered system modeling localization of quantum waves in random media. We will show that the transport properties of several natural Hamiltonians on metric and discrete trees with random branching numbers are suppressed by disorder. This phenomenon is called Anderson localization.

https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Abstract:

The event will have graduate students speaking about their experiences with their internships.

The facilitator of the event is Montie Averie.

The participants of the Graduate Student Internship Panel will be:

Carter Chain (interned at Travelers)

Brendan Cook (interned at Target)

Ty Frazier (interned at Securian Financial and Lawrence Berkeley national lab)

Jacob Hegna (interned at Google)

Sarah Milstein (interned at Ayasdi, 3M, IDA, Cargill and Smart Information Flow Technologies (SIFT))

Amber Yuan (interned at Argonne national lab,  ExxonMobil  and Activision Blizzard).

The event is organized by the SIAM Student Chapter at the University of Minnesota.

Abstract:

In water-limited regions, competition for water resources results in the formation of vegetation patterns; on sloped terrain, one finds that the vegetation typically aligns in stripes or arcs. The dynamics of these patterns can be modeled by reaction-diffusion PDEs describing the interplay of vegetation and water resources, where sloped terrain is modeled through advection terms representing the downhill flow of water. We focus on one such model in the 'large-advection' limit, and we prove the existence of traveling planar stripe patterns using analytical and geometric techniques. We also discuss implications for the stability of the resulting patterns, as well as the appearance of curved stripe solutions.

Abstract:

I'll present a heuristic for finding special families of partially ordered sets. The heuristic says that the posets with order polynomial product formulas are the same as the posets with good dynamical behavior. Here the order polynomial is a certain enumerative invariant of the poset. Meanwhile, the dynamics includes promotion of linear extensions, and rowmotion of order ideals and P-partitions. This talk includes joint work with Tri Lai, and with Martin Rubey.

see seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html

Abstract:

We will briefly review, through two examples, classic deterministic PDE models of population dynamics structured according to attributes such as age and/or size. First, we describe how the original McKendrick model was used to motivate China's one-child policy, and generalize it to include an imposed, finite interbirth refractory period. We quantify the effectiveness of this softer, staggered birth policy and discuss its predicted effectiveness. We then review sizer-timer-adder-type models used to quantify proliferating cell populations. Here, blow-up in mean cell sizes can arise, which represents a challenging numerical problem. Finally, we extend these classic deterministic models to allow for both demographic and growth-rate stochasticity by developing a fully kinetic theory. Marginalization of the full density functions results in a set of coupled kinetic models similar to the BBGKY hierarchy. We map out the different combinations of stochastic descriptions and show how the classic age-dependent population models are connected to this hierarchy, the lowest order of which is a master equation for the total stochastic population. Differences in the stochastic description of birth through budding or splitting are explored.

Abstract:

In this talk, we will derive a priori interior Hessian estimates for the Lagrangian mean curvature equation under certain natural restrictions on the Lagrangian phase. As an application, we will use these estimates to solve the Dirichlet problem for the Lagrangian mean curvature equation with continuous boundary data, on a uniformly convex, bounded domain in R^n.

Abstract:

The need for fairness, accountability, and transparency in computer models that make or inform decisions about people has become increasingly clear over the last several years. One application area where these topics are particularly important is criminal justice, as statistical models are being used to make or inform decisions that impact highly consequential decisions— those concerning an individual’s freedom. In this talk, I’ll highlight three threads of my own research into the use of machine learning and a statistical models in criminal justice models that demonstrate the importance of careful attention to fairness, accountability, and transparency. In particular, I’ll discuss how predictive policing has the potential to reinforce and amplify unfair policing practices of the past. I’ll also discuss some of the ways in which recidivism prediction models can fail to require the accountability and transparency necessary to prevent gaming.

Kristian Lum is on the faculty at University of Pennsylvania's School of Engineering and Applied Science and is the former Lead Statistician at the Human Rights Data Analysis Group (HRDAG). Kristian’s research primarily focuses on examining the uses of machine learning in the criminal justice system, including demonstrating the potential for predictive policing models to reinforce and amplify historical racial biases in law enforcement. She has also served on Research Advisory Councils for the New York City’s Mayor’s Office of Criminal Justice and Philadelphia’s First Judicial District tasked with advising on the development of fairer algorithmic pre-trial risk assessments.

Kristian holds an M.S. and Ph.D. from the Department of Statistical Science at Duke University and a B.A. in Mathematics and Statistics from Rice University.

Abstract:

The spread of epidemics is a very complex process, and stochastic diffusion models on networks have been found useful, especially when modeling their spread in large and heterogeneous populations, where individual and community level behaviors need to be represented. A fundamental problem in such models is to understand how to control the spread of an epidemic by interventions such as vaccination (which can be modeled as node removal) and social distancing (which can be modeled as edge removal). A number of heuristics have been studied, such as selecting nodes based on degree and eigenscore. However, rigorous algorithms with approximation guarantees are not well understood, and is the focus of this talk.

We will discuss two approaches for epidemic control from a network science perspective. The first involves reducing the spectral radius of the graph, motivated by a characterization that shows that epidemics in some models die out fast if the spectral radius is below a threshold. We discuss algorithms for this problem and its generalizations. The second approach involves stochastic optimization, using a sample average approximation combined with rounding. We show that this approach gives near optimal solutions in practice, and have interesting structural properties, which might be useful
in finding practical interventions.

Anil Vullikanti is a Professor in the Department. of Computer Science and the Biocomplexity Institute at the University of Virginia. His research interests are in the broad areas of network science, dynamical systems, combinatorial optimization, and distributed computing, and their applications to computational epidemiology and social networks.

Abstract:

As states begin to reopen, there is an urgent need for
COVID-19 projections that can guide decision-makers in relaxing
restrictions in a way that minimizes the chance of resurgence. Though
researchers have access to a wide variety of mathematical infectious
disease transmission models, limited data and uncertainties about
epidemiological features of COVID-19 make statistical calibration of
these models challenging. Futhermore, decision-makers are often more
interested in future projections under specified re-opening scenarios
than in estimated parameter values. In this presentation, I outline
mathematical and statistical approaches for projecting COVID-19
incidence, hospitalization, and deaths. I describe a simple class of
transmission models that balance parsimony with epidemiological
realism for the epidemic in Connecticut. Using unique access to data
from Connecticut, and information about the Governor's stated
reopening plans, we find that closure of schools and the statewide
“Stay Safe, Stay Home” order have effectively reduced COVID-19
transmission in Connecticut, with model projections estimating
incidence at about 1,500 new infections per day. If close
interpersonal contact increases quickly in Connecticut following
reopening on May 20, the state is at risk of a substantial increase
COVID-19 infections, hospitalizations, and deaths by late Summer 2020.
However, real-time metrics including case counts, hospitalizations,
and deaths may fail to provide enough advance warning to avoid
resurgence. Substantial uncertainty remains in our knowledge of
cumulative COVID-19 incidence, the proportion of infected individuals
who are asymptomatic, infectiousness of children, the effects of
testing and contact tracing on isolation of infected individuals, and
how contact patterns may change following reopening.

Abstract:

Abstract:

One of the most far reaching proofs of Cayley's formula, that the number n^{n-2} counts trees on n labeled vertices, is via Kirchhoff's Matrix Tree theorem. After Denes, Schaeffer, and many others, there is a well-exploited correspondence between trees and transitive factorizations in the symmetric group; in particular, the number n^{n-2} counts shortest factorizations of the long cycle (12..n) in transpositions. Furthermore, Burman and Zvonkine (and independently Alon and Kozma) have given a "higher-genus" formula that enumerates arbitrary length factorizations of long cycles, where each transposition (ij) is weighted by its own variable w_ij, and which has a product form involving the eigenvalues of the Laplacian L(K_n) of the complete graph.In joint work with Guillaume Chapuy, we consider a (partial) analog of the weighted Laplacian for complex reflection groups W. The weights are specified via any given flag of parabolic subgroups, generalizing the definition of Jucys-Murphy elements. We prove a product formula for the enumeration of weighted reflection factorizations of Coxeter elements, that subsumes the Chapuy-Stump formula and in part the Burman-Zvonkine formula. Its proof is based on an interesting fact that relates the exterior powers of the reflection representation with those W-characters that are non-zero on the Coxeter class. We present some further applications of these techniques, in particular, a uniform simple(r) way to produce the chain number h^n*n!/|W| of the noncrossing lattice NC(W). An extended abstract for this work was accepted for FPSAC 2020 and is available at my website (https://www.irif.fr/~douvr001/).

Abstract:

Two kinds of singular transformations of a rotationally invariant \alpha-stable process (x(t))_{t \ge 0} in a d-dimensional Euclidean space R^d are considered. They are both connected with the notion of a local time on a given surface S in R d for the process (x(t))_{t \ge 0} (it is supposed that \alpha \in (1, 2) and d \ge 2). The first transformation is determined by a given continuous function (p(x))_{x \in S} with non-negative values and it consists in killing the process (x(t))_{t \ge 0} at a point x \in S with “the intensity p(x)”. This kind of membranes can be called an elastic screen by analogy to that in the theory of diffusion processes. The second transformation is likewise determined by a given function (p(x))_{x \in S} with positive values and its result is the process (x(t))_{t \ge 0} for which any point x \in S is sticky with “the intensity r(x)”. It is shown that each one of these membranes is associated with some initial-boundary value problem for a pseudo-differential equation related to the process (x(t))_{t \ge 0}. These facts are established with the help of some generalization of classical theory of single-layer potentials for situations where, instead of differential, the pseudo-differential equation mentioned above is considered.

Abstract:

Testing django 2.2 upgrade