Title: Symplectic Capacities and Volume Radius

Abstract: In this talk we discuss a conjecture of Viterbo relating the symplectic capacity of a convex body and its volume. The conjecture states that among all the 2n-dimensional convex bodies with a given volume the Euclidean ball has maximal symplectic capacity. In a joint work with Shiri Artstein-Avidan and Vitali Milman, we bring together tools and ideology from asymptotic geometric analysis and verify the above conjecture up to a universal constant.