Program:
10:00-11:00 Tails of Martingale Limits in Branching Random Walk (by Xinxin Chen, Beijing Normal University)
11:30-12:30 Approximate Controllability of PDEs Using Degenerate Forces (by Vahagn Nersesyan, NYU Shanghai)
12:30-14:30 Lunch Break
14:30-15:30 Machine Learning For Master Equations in Mean Field Games (by Mathieu Laurière, NYU Shanghai)
16:00-17:00 Global Control of Geometric Equations (by Shengquan Xiang, Peking University)
Tails of Martingale Limits in Branching Random Walk
Xinxin Chen, Beijing Normal University
Short Biography:
Xinxin Chen is currently Professor at Beijing Normal University. She obtained her Bachelor's Degree in Mathematics from Tsinghua University in 2009 and received her Ph.D. Degree from Université Pierre et Marie Curie (Paris VI) in 2014. She then worked at the Université Claude Bernard Lyon 1 from 2014 to 2021. Chen’s main research interests include Branching random walks and Random walk in random environment.
Approximate Controllability of PDEs Using Degenerate Forces
Vahagn Nersesyan, NYU Shanghai
Abstract:
In this talk, we will review some recent results on the controllability of PDEs using degenerate forces. In the case when the control force acts in the whole domain, we will see how approximate controllability can be established by applying large finite-dimensional controls on small time intervals through a carefully chosen scaling. We will also discuss some results where PDEs are controlled using degenerate forces applied only in a small region of the domain. This talk is partially based on joint works with Manuel Rissel.
Short Biography:
Vahagn Nersesyan is an Associate Professor of Mathematics at NYU Shanghai. Prior to joining NYU Shanghai, he was a Maitre de conferences at University of Paris-Saclay. He obtained his PhD from University of Paris XI and Habilitation thesis from University of Versailles. His main research interests are in the intersection of Probability Theory and Partial Differential Equations.
Machine Learning For Master Equations in Mean Field Games
Mathieu Laurière, NYU Shanghai
Abstract:
Mean field games have been introduced to study games with many players. Since their introduction, they have found numerous potential applications and the theory has been extensively developed. While forward-backward systems of partial or stochastic differential equations can be used to characterize Nash equilibria with a fixed initial distribution, the Master equation introduced by P.-L. Lions provides a tool to solve the problem globally, for any initial condition. However this equation is a partial differential equation posed on the space of measures, which raises significant challenges to solve it numerically. In this talk, we will present several computational methods that have been proposed to tackle Master equations. Theoretical convergence results and numerical experiments will be presented.
Short Biography:
Mathieu Laurière is an Assistant Professor of Mathematics and Data Science at NYU Shanghai. Prior to joining NYU Shanghai, he was a Postdoctoral Research Associate at Princeton University in the Operations Research and Financial Engineering (ORFE) department. He obtained his MS from Sorbonne University and ENS Paris-Saclay and his PhD from the University of Paris. Before joining Princeton University, he was a Postdoctoral Fellow at the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai. Most recently, Mathieu was a Visiting Faculty Researcher at Google Brain, for the Brain Team (Paris).
Global Control of Geometric Equations
Shengquan Xiang, Peking University
Abstract:
Recently, together with Coron and Krieger, we initiated a topic on the global control of geometric equations, first on wave map equations and then on the harmnic map heat flow. Combining ideas from control theory, heat flow, differential geometry, and asymptotic analysis, we obtain several important properties, such as small-time local controllability, local quantitative rapid stabilization, obstruction to semi-global asymptotic stabilization, and global controllability to geodesics. Surprisingly, due to the geometric feature of the equation we also discover the small-time global controllability between harmonic maps within the same homotopy class for general compact Riemannian manifold targets, which is to be compared with the analogous but longstanding problem for the nonlinear heat equations.
Short Biography:
Shengquan Xiang is an Assistant Professor at Peking University. He received his Ph.D. from the Sorbonne Universite under the supervision of Prof. Jean-Michel Coron. His research interests focus on partial differential equations and related control problems.
Event by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.