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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

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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…

Biomathematics Seminar: Justin Lessler, UNC, What are planning scenarios for and how can we evaluate them?

Cox 306

As with weather, there is a limit to how far into the future we can accurately forecast the future course of epidemics. Yet, we often need to make plans further into the future than we can reasonably forecast, and in many cases our actions themselves will change the course of an epidemic. One solution to this conundrum is the construction of "planning scenarios" where we project the likely course of an epidemic well beyond the…

Algebra and Combinatorics Seminar: Yupeng Li, Duke University, Coparking functions for matroids

SAS 3282

In Stanley’s seminal work “Cohen-Macaulay Complexes”, Stanley conjectured that all h vectors of matroid complexes are pure O-sequences. We constructed coparking functions on matroids with extra restrictions and showed that the degree sequences of coparking functions are the same as h vectors of matroid complexes. By this construction, we proved that Stanley’s conjecture is true…

Differential Equations and Nonlinear Analysis Seminar: Thierry Champion, University of Toulon, France,Relaxed multi-marginal costs in optimal transport and quantization effects

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 In this talk, I shall present a relaxation formula and duality theory for the multi-marginal Coulomb cost that appears in optimal transport problems arising in Density Functional Theory. The related optimization problems involve probabilities on the entire space and, as minimizing sequences may lose mass at infinity, it is natural to expect relaxed solutions which…

Computational and Applied Mathematics Seminar: Maria Lukacova, the University of Mainz, Uncertainty Quantification for Low Mach Number Flows

SAS 4201

We consider weakly compressible flows coupled with a cloud system that models the dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertainties that arise due to unknown input data, such as model parameters and initial or boundary conditions. The developed stochastic Galerkin method combines the space-time approximation obtained by a…