Geometric PDE and Applied Analysis Seminar (August 19, 2026)

Title: Game-theoretic approaches to partial differential equations and related problems

Speaker: Prof. Jeongmin Han (Soongsil University)

Abstract: Probabilistic approaches have long been one of the powerful tools in the study of PDEs. They not only provide an alternative perspective for understanding these equations but have also led to new mathematical developments in the field. A classic example is the use of random walks in the study of the Laplace equation, where the mean value property of harmonic functions serves as the key connection.  Similar ideas can be extended to a broader class of equations. In the nonlinear setting, the so-called tug-of-war game provides a representative example. This stochastic game can be interpreted as a discretization scheme for the normalized p-Laplace operator.

In this talk, I will mainly discuss recent research on p-Laplace type PDEs and related problems from the perspective of tug-of-war games. More recently, game-theoretic approaches have also been applied to a wider range of PDEs and neighboring areas, and I will briefly touch upon some of these developments as well.