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…
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…
INVITATION TO MATHEMATICS GRADUATION CEREMONY
North Carolina State University Reception for Alumni and Friends of the Department of Mathematics Thursday, January 4 6:00 - 8:00 pm San Francisco Marriott Marquis, Salon 3
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.…
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…
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.…
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…
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…
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…
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…
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…
Virtual (Zoom link: https://ncsu.zoom.us/j/93542716306?pwd=c1Iyc0s2bUJhWUR0R2ZNcmlLSHJqQT09)
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…
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…
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.
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.