A tale of two conjectures: from Mahler to Viterbo.

In this talk we explain how billiard dynamics can be used to relate a symplectic isoperimetric-type conjecture by Viterbo with an 80-years old open conjecture by Mahler regarding the volume product of convex bodies. The talk is based on a joint work with Shiri Artstein-Avidan and Roman Karasev.