Symplectic Tiling Billiards on Complete Affine Tori

Symplectic tiling billiards is a game played on a tiling of the plane that only relies on a notion of parallelism and lends itself to study under the more general non-Euclidean affine structures of the torus. In this talk we will address the classification of affine structures on the torus and how to use them to play symplectic tiling billiards. Demonstrations of the game will be provided in real time along with arguments to explain observed behavior of orbits. This is joint with Fabian Lander.