Elastic Shape Analysis of Curves and Surfaces

In this talk, I will discuss large population stochastic games defined on finite state spaces and introduce the associated limiting framework known as mean field games, which characterize the equilibrium behavior as the population size grows. I will present both partial differential equations (PDEs) and probabilistic approaches for analyzing and finding equilibria in mean field games. Finally, I will showcase several neural network-based methods for numerically solving these mean field game models, highlighting their effectiveness and potential applications. This talk is based on joint works with Erhan Bayraktar, William Hofgard, Mathieu Lauriere, and Ethan Zell.