Colloquium: Tuesday, January 12, 2 pm. Speaker: Yaron Ostrover (Tel Aviv) . Title: “From symplectic measurements to Mahler’s conjecture via billiard dynamics”.

We shall discuss certain symplectic invariants known as symplectic capacities.
In particular, we will show how these invariants in the classical phase space 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 a 70-years old
open conjecture by Mahler regarding the volume product of convex sets. Based on a joint work
with Shiri Artstein-Avidan and Roman Karasev. No prior knowledge of symplectic geometry
will be required.