A Symplectic Perspective on Minkowski Billiard Dynamics

Speaker. Yaron Ostrover
Date. 26.09.23 at 14:30

Abstract. We will discuss some relations between symplectic invariants known as symplectic capacities and Minkowski billiard dynamics. In particular, we will show how these invariants can be used to obtain information on the length of the shortest periodic billiard trajectory in a smooth convex domain, and how a symplectic isoperimetric conjecture by Viterbo is related to an 80-year-old open conjecture by Mahler regarding the volume product of convex sets. This is based on joint works with Shiri Artstein-Avidan and Roman Karasev.