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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…

Geometry and Topology Seminar: Ao Sun, Lehigh University, Interpolation method in mean curvature flow

Zoom

The interpolation method is a very powerful tool to construct special solutions in geometric analysis. I will present two applications in mean curvature flow: one is constructing a new genus one self-shrinking mean curvature flow, and another one is constructing immortal mean curvature flow with higher multiplicity convergence. The talk is based on joint work…

Algebra and Combinatorics Seminar: Yairon Cid-Ruiz, NC State, Duality and blow-up algebras

SAS 4201

We provide a generalization of Jouanolou duality that is applicable to a plethora of situations. The environment where this generalized duality takes place is a new class of rings, that we introduce and call weakly Gorenstein. As a main consequence, we obtain a new general framework to investigate blowup algebras. We use our results to…

Differential Equations and Nonlinear Analysis Seminar: Nicolás García Trillos, University of Wisconsin Madison

SAS 4201

Despite the success of deep learning-based algorithms, it is widely known that neural networks may fail to be robust to adversarial perturbations of data. In response to this, a popular paradigm that has been developed to enforce robustness of learning models is adversarial training (AT), but this paradigm introduces many computational and theoretical difficulties. Recent…

Kwangil Koh Lecture on Mathematics in Our Time: Robert Ghrist, University of Pennsylvania, Information Dynamics on Social Networks

SAS 2203

Abstract: Social networks play a crucial role in how we share and discuss ideas. This talk delves into the mathematics behind the spread of information (such as opinions or beliefs) on these networks. Imagine a network as a complex web, where each node represents an individual and the connections represent interactions. Opinions, beliefs, arguments, and other…

Stochastics Seminar: Shankar Bhamidi, UNC at Chapel Hill, Dynamic networks and stochastic approximation

SAS 4201

 Models for networks that evolve and change over time are ubiquitous in a host of domains including modeling social networks, understanding the evolution of systems in proteomics, the study of the growth and spread of epidemics etc. This talk will give a brief summary of three recent findings in this area where stochastic approximation techniques…

Applied Math Graduate Student Seminar – Introductory and Organizational Meeting

SAS 4201

If you are interested in learning more about applied math research from your fellow students, or you want a friendly and constructive environment to practice presenting your own research, AMGSS is for you! This is an informational and sign-up meeting, so come to learn more about AMGSS and/or to sign up to present your research.

Geometry and Topology: Peter McGrath, NC State, New Minimal Surfaces in B^3

SAS 4201

A fundamental question in Differential Geometry which has spurred much recent work is whether every orientable compact surface with boundary can be minimally embedded in the Euclidean 3-ball with free boundary.  I will discuss work (joint with M. Karpukhin, R. Kusner, and D. Stern)  which resolves this problem.

Teaching and Learning Seminar: Catie Acitelli, Notre Dame, The Development and Implementation of New Applied Math Curricula

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 Computational and applied mathematics are growing in popularity and relevance.  As students prepare for either the job market or graduate school, it is increasingly more important that their mathematics courses reflect the changing landscape of the field.  In this talk, I will detail my development and initial implementation of two new courses: Applied Calculus I…

Computational and Applied Mathematics Seminar: Alexander Kurganov, SUSTech, Central-Upwind Schemes with Reduced Numerical Dissipation

SAS 4201

Central-upwind schemes are Riemann-problem-solver-free Godunov-type finite-volume schemes, which are, in fact, non-oscillatory central schemes with a certain upwind flavor: derivation of the central-upwind numerical fluxes is based on the one-sided local speeds of propagation, which can be estimated using the largest and smallest eigenvalues of the Jacobian. I will introduce two new classes of central-upwind…

Stochastics Seminar: Dominykas Norgilas, NC State, How expensive can an American option be?

SAS 4201

The goal of this talk is to price American-type financial contracts in the presence of Knightian uncertainty. In particular, instead of choosing a particular probabilistic model to represent the price process of some underlying asset (on which an American option is written), we first restrict our attention to the whole class of models that are…

Applied Math Graduate Student Seminar: T.H. Molena Nguyen, NC State, Parallel Recursive Skeletonization Solver for Dense Linear Systems on GPU-Accelerated Computers

SAS 4201

Dense linear systems in large-scale kernel approximation in machine learning, discretization of boundary integral equations in mathematical physics, and low-rank approximation of Schur complements in large sparse matrix factorization often employ a multilevel structure of low-rank off-diagonal blocks. To solve such systems efficiently, we present a GPU-based parallel recursive skeletonization solver that utilizes batched dense…