Title: Game-theoretic approaches to partial differential equations and related problems (starts 9.00 sharp)
Abstract: Probabilistic approaches have long been one of the powerful tools in the study of PDEs.
It not only offers an alternative perspective for understanding these equations but has also contributed to new mathematical developments in the field.
A classical 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 applied 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 discretized scheme for the normalized p-Laplace operator.
In this talk, I will mainly discuss research on p-Laplace type PDEs and related problems approached through tug-of-war.
Recently, such game-theoretic approaches have also been actively employed in exploring other PDEs and neighboring areas, and I will touch upon some of these developments as well.
