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Differential Equations and Nonlinear Analysis Seminar: Tu Nguyen Thai Son, Michigan State University, Generalized convergence of solutions for nonlinear Hamilton-Jacobi equations

SAS 4201

We examine the asymptotic behaviors of solutions to Hamilton-Jacobi equations while varying the underlying domains. We establish a connection between the convergence of these solutions and the regularity of the additive eigenvalues in relation to the domains. To accomplish this, we introduce a framework based on Mather measures that enables us to compute the one-sided derivative…

Computational and Applied Mathematics Seminar: Antoine Blanchard, Verisk, A Multi-Scale Deep Learning Framework for Projecting Weather Extremes

Zoom

Extreme weather events are of growing concern for societies because under climate change their frequency and intensity are expected to increase significantly. Unfortunately, general circulation models (GCMs)--currently the primary tool for climate projections--cannot characterize weather extremes accurately. Here, we report on advances in the application of a multi-scale deep learning framework, trained on reanalysis data,…

Geometry and Topology Seminar: Andrew Shedlock, NC State, Recovery of a complete Riemannian Manifold using the local source-to-solution operator for the Electro-Magnetic Wave Operator

SAS 1216

In this talk we consider an Electro-Magnetic Wave operator on a complete Riemannian manifold, which generalizes the standard wave equation to include first order and zeroth order terms.  The Cauchy Problem for the Electro-Magnetic Wave operator with zero initial values and a smooth compactly supported forcing function has a unique smooth solution. We study the…

Geometry and Topology Seminar: Lili Yan, University of Minnesota, Stable determination of time-dependent collision kernel in the nonlinear Boltzmann equation

SAS 1216

In this talk, we consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions 2 and higher. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional conditions. A uniqueness result is derived as an immediate consequence of the stability result. Our approach relies on…

Applied Math Graduate Student Seminar: Sam Thornton, NC State, Dual-Domain Clustering of Spatiotemporal Infectious Disease Data

SAS 4201

The purpose of this project is to develop, test, and document performance of dual-domain clustering algorithms for spatiotemporal datasets, tailored to pandemic preparedness and endgame challenges. Dual-domain clustering refers to the unsupervised learning clustering method performed on data with both application-specific attributes (e.g., number of infectious) and geographic information (e.g., latitude and longitude of data…

Colloquium: Christopher K.R.T. Jones, University of North Carolina at Chapel Hill, Do We Need to Adapt to a Changing Climate, or to the Rate at Which it is Changing?

SAS 4201

The climate is changing due to the heat trapping caused by the rapid increase in greenhouse gases, mainly carbon dioxide, in the atmosphere. One way to state the issue is that we cannot, as a species, adapt to the new conditions quickly enough. This is an example of rate-induced tipping for which the mathematics has…

Algebra and Combinatorics Seminar: Raymond Maresca, Brandeis University, Combinatorics of exceptional collections in type A-tilde

SAS 4201

We will define quivers of type A-tilde, their representations, and exceptional collections of these representations. We will then introduce a combinatorial model of these representations, based on the one constructed by Garver, Igusa, Matherne, and Ostroff for type A, by drawing strands on a copy of the integers. We will see that collections of strands…

Differential Equations and Nonlinear Analysis Seminar: Anna Doubova, University of Seville, Inverse problems connected with Burgers equation and some related systems

Zoom

We consider inverse problems concerning the one-dimensional viscous Burgers equation and some related nonlinear systems (involving heat effects, variable density, and fluid-solid interaction). We are dealing with inverse problems in which the goal is to find the size of the spatial interval from some appropriate boundary observations. Depending on the properties of the initial and…

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

Zoom

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…