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Differential Equations and Nonlinear Analysis Seminar: Edouard Pauwels, Université de Toulouse, Nonsmooth differentiation of parametric fixed points

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Recent developments in the practice of numerical programming require optimization problems not only to be solved numerically, but also to be differentiated. This allows to integrate the computational operation of evaluating a solution in larger models, which are themselves trained or optimized using gradient methods. Most well known applications include bilevel optimization and implicit input-output…

Computational and Applied Mathematics – Differential Equations and Nonlinear Analysis Seminar: Alexey Miroshnikov, Discover Financial Services, Stability theory of game-theoretic group feature explanations for machine learning models.

SAS 4201

In this article, we study feature attributions of Machine Learning (ML) models originating from linear game values and coalitional values defined as operators on appropriate functional spaces. The main focus is on random games based on the conditional and marginal expectations. The first part of our work formulates a stability theory for these explanation operators…

Stochastics Seminar: Amarjit Budhiraja, UNC-Chapel Hill, Large deviations for weakly interacting diffusions and mean field stochastic control problems

SAS 4201

Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is common to all particles. The interaction between the particles is due to the common noise and…

Algebra and Combinatorics Seminar: Maximilian Kaipel, University of Cologne, Partitioned fans, hyperplane arrangements and K(pi,1) spaces

SAS 4201

Polyhedral fans are geometric objects, which arise naturally in many areas of mathematics, for example in toric geometry, the theory of hyperplane arrangements and representation theory. In many cases, there are natural ways of identifying some of the polyhedral cones defining a fan, thus giving a "partition of the fan". To each such partitioned fan…

Differential Equations and Nonlinear Analysis Seminar: Wojciech Ozanski, FSU, Logarithmic spiral vortex sheets

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We will discuss a special family of 2D incompressible inviscid fluid flows in the form of logarithmic spiral vortex sheets. Such flows are determined by a vorticity distribution of a curve R^2, and they are notoriously hard to study analytically. In the talk we will discuss several results regarding logarithmic spiral vortex sheets: well-posedness of the spirals as…

Colloquium: Gadi Fibich, Tel Avis University, Effects of Network Structure on Spreading of Innovations

SAS 4201

Spreading (diffusion) of new products is a classical problem. Traditionally, it has been analyzed using the compartmental Bass model, which implicitly assumes that all individuals are homogeneous and connected to each other. To relax these assumptions, research has gradually shifted to the more fundamental Bass model on networks, which is a particle model for the…

Financial Mathematics Seminar: Xunyu Zhou, Columbia University, Learning Merton’s Strategies in an Incomplete Market

SAS 1102

We study Merton’s expected utility maximization problem in an incomplete market, characterized by a factor process in addition to the stock price process, where all the model primitives are unknown. We take the reinforcement learning (RL) approach to learn optimal portfolio policies directly by exploring the unknown market, without attempting to estimate the model parameters.…

Applied Math Graduate Student Seminar: Harley Hanes, NC State, Boundary Penalties, Sensitivity Equation Projection, and Optimal Sample Identification in Reduced-Order Models

SAS 4201

Reduced-order models (ROMs) are a critical tool for sensitivity analysis, parameter inference, and uncertainty quantification where high-fidelity models would be computationally intractable. Galerkin POD-ROMs are one particular class of ROMs which project high-fidelity model equations onto a set of model solutions to construct ROMs retaining original model parameters and physics, enabling accurate sensitivity analysis, parameter inference,…

Biomathematics Seminar: Jichun Xie, Duke, Disentangling Cellular Heterogeneities and Activities from the Topology Structures of Single-cell Co-expression Graphs

Cox 306

Gene co-expression graphs are a rich source of information, revealing critical insights into cellular functions, states, and activities. Yet, extracting meaningful signals from these graphs presents a formidable challenge. This complexity arises due to the presence of multiple, overlapping sources of information and the inherent noise, which is particularly pronounced in data derived from single-cell…

Geometry and Topology Seminar: Salem Selim, UC Irvine, Partial data inverse problems for magnetic Schrödinger operators with potentials of low regularity.

SAS 4201

In this talk we discuss partial data inverse boundary problems for magnetic Schrödinger operators on bounded domains in the Euclidean space as well as some Riemannian manifolds with boundary. In particular, we show that the knowledge of the set of the Cauchy data on a portion of the boundary of a domain in the Euclidean…

Algebra and Combinatorics Seminar: Emily Barnard, DePaul University, Pop-stack sorting and pattern-avoiding permutations

SAS 4201

The pop-stack sorting method takes an ordered list or permutation and reverses each descending run without changing their relative positions. In this talk we will review recent combinatorial results on the pop-stack sorting method, and we will extend the pop-stack sorting method to certain pattern avoiding permutations, called c-sortable. If time permits, we will describe…

Differential Equations and Nonlinear Analysis Seminar: Hung Tran, University of Wisconsin Madison, Periodic homogenization of Hamilton-Jacobi equations: some recent progress

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I first give a quick introduction to front propagations, Hamilton-Jacobi equations, level-set forced mean curvature flows, and homogenization theory. I will then show the optimal rates of convergence for homogenization of both first-order and second-order Hamilton-Jacobi equations. Based on joint works with J. Qian, T. Sprekeler, and Y. Yu. Zoom meeting: Link

Computational and Applied Mathematics Seminar: Wenjing Liao, Georgia Institute of Technology, Exploiting Low-Dimensional Data Structures in Deep Learning

SAS 4201

In the past decade, deep learning has made astonishing breakthroughs in various real-world applications. It is a common belief that deep neural networks are good at learning various geometric structures hidden in data sets. One of the central interests in deep learning theory is to understand why deep neural networks are successful, and how they…