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Computational and Applied Mathematics Seminar: Gabriel P. Langlois, Courant Institute, An exact and efficient algorithm for the Lasso regression problem based on a Hamilton-Jacobi PDE formulation

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The Basis Pursuit Denoising problem, also known as the least absolute shrinkage and selection operator (Lasso) problem, is a cornerstone of compressive sensing, statistics and machine learning. In high-dimensional problems, recovering an exact sparse solution requires robust and efficient optimization algorithms. State-of-the-art algorithms for the Basis Pursuit Denoising problem, however, were not traditionally designed to…

Stochastics Seminar: Erik Bates, NC State, The Busemann process of (1+1)-dimensional directed polymers

SAS 4201

Directed polymers are a statistical mechanics model for random growth.  Their partition functions are solutions to a discrete stochastic heat equation.  This talk will discuss their logarithmic derivatives, which are solutions to a discrete stochastic Burgers equation.  Of interest is the success or failure of the  "one force-one solution principle" for this equation.  I will…

Stochastics Seminar: Evan Sorensen, Columbia University, Jointly invariant measures for the Kardar-Parisi-Zhang Equation

SAS 4201

We give an explicit description of the jointly invariant measures for the KPZ equation. These are couplings of Brownian motions with drift, and can be extended to a process defined for all drift parameters simultaneously. We term this process the KPZ horizon (KPZH). As a corollary of this description, we resolve a recent conjecture of…

Biomathematics Seminar: Kyle Nguyen, NC State

Cox 306

All BMA seminars have a virtual option with the following Zoom Link: https://ncsu.zoom.us/j/93046132033?pwd=dkZiTjlKazgzK2Q3aXJra1g2R1Q0dz09 Meeting ID: 930 4613 2033 Passcode: 075251

Algebra and Combinatorics Seminar: Adam Daniel Gregory, University of Florida,Vexillary double Edelman–Greene coefficients are Graham positive

SAS 4201

Lam, Lee, and Shimozono (LLS) recently introduced backstable double Schubert polynomials to represent classes in the cohomology ring of the infinite flag variety. Using these polynomials, they introduce double Stanley symmetric functions, which expand into double Schur functions with polynomial coefficients called double Edelman--Greene coefficients. They prove that double Edelman--Greene coefficients are Graham positive. For…

Differential Equations and Nonlinear Analysis Seminar: Benjamin Seeger, University of Texas at Austin, Weak solutions of nonlinear, nonconservative transport systems

SAS 4201

I will discuss certain systems of transport type whose coefficients depend nonlinearly on the solution. Applications of such systems range from the modeling of pressure-less gases to the study of mean field games in a discrete state space. I will identify a notion of weak solution within the class of coordinate-wise decreasing functions, a condition…

Stochastics Seminar: Khai Nguyen, NC State, Differential Game Models of Optimal Debt Management

SAS 4201

In this talk, I will present recent results on game theoretical formulation of optimal debt management problems in an infinite time horizon with exponential discount, modeled as a noncooperative interaction between a borrower and a pool of risk-neutral lenders. Here, the yearly income of the borrower is governed by a stochastic process and bankruptcy instantly occurs…

Applied Math Graduate Student Seminar: John Darges, NC State, Randomized Function Approximation

SAS 4201

Two of the most popular approaches to supervised learning are kernels and artificial neural networks (ANN).The ability to emulate complicated nonlinear behavior makes them powerful tools for function approximation.Randomization schemes, which have been successfully deployed to improve efficiency for many algorithms, havealso been developed for kernel methods and ANNs. These are random weight neural networks…

Geometry Topology Seminar: Paweł Dłotko, DIOSCURI Centre for Topological Data Analysis, Warsaw, Poland, From Euer number to statistics and back. Tangential approach to Topological Data Analysis.

SAS 4201

In this talk, I will give a brief and intuitive overview of the methods of Topological Data Analysis we developed in my Discuri Centre. Starting from Euler numbers and its generalization we will get to the regime of statistical goodness of fit test. We will explore alternative methods of constructing graph based visualization of data.…

Biomath Seminar: Siting Liu, UCLA, An inverse problem in mean field game from partial boundary measurement

Cox 306

Mean-field game (MFG) systems provide a powerful framework for modeling the collective behavior of multi-agent systems with diverse applications, including those in biological populations. However, unknown parameters pose challenges. In this work, we tackle an inverse problem, recovering MFG parameters from limited, noisy boundary observations. Despite the problem's ill-posed nature, we aim to efficiently retrieve…

Algebra and Combinatorics Seminar: Michael Hull, UNC Greensboro, Highly transitive groups, hyperbolicity, and random walks

SAS 4201

A group is highly transitive if it admits a faithful, highly transitive action, that is an action which is k-transitive for all k>0. We will discuss some algebraic properties of these groups, as well as constructions of highly transitive actions for hyperbolic groups (and a wide array of generalizations of hyperbolic groups) using random walks.…

Computational and Applied Mathematics: Jingwei Hu, University of Washington, Structure-Preserving Particle Method for the Vlasov-Maxwell-Landau Equation

SAS 4201

The Vlasov-Maxwell-Landau equation is often regarded as the first-principle physics model for plasmas. We introduce a novel particle method for this equation that collectively models particle transport, electromagnetic field effects, and particle collisions. The method arises from a regularization of the variational formulation of the Landau collision operator, leading to a discretization of the operator…