The M-ellipsoid, Symplectic Capacities and Volume
  In this work we bring together tools and ideology from two different fields, Symplectic Geometry and Asymptotic Geometric Analysis, to arrive at some new results. Our main result is a dimension-independent bound for the symplectic capacity of a convex body by its volume radius. 
Shiri Artstein-Avidan, Vitali D. Milman and Yaron Ostrover