Day/Time: Friday at 5pm Plenary Lecture:

"Tug-of-War games and PDEs"

Abstract:
The purpose of this talk is to explain the recently discovered connection between the theory of discrete (stochastic) Tug-of-War games and the non-linear (deterministic) Partial Differential Equations. Roughly speaking, it turns out that solutions to certain complicated PDEs can be interpreted as 'values' of Tug-of-War games (i.e. how much money one player pays to the other at the end of the game), in the limit when the scale of the 'checkerboard' on which the game is played goes to zero (i.e. when the rules of the game allow only for smaller and smaller distances that the token can be 'tugged' by one of the players in her preferred direction). This intricate connection was first understood by Peres, Sheffield, Schramm, and Wilson in 2009, and it subsequently opened the door to deep applications and new beautiful observations in the Mathematical Analysis and PDEs.