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.