Mathematical Conversations

Convexity plays a central role in several geometric and dynamical problems in symplectic geometry. However, convexity is not preserved under structure preserving isomorphisms and it is unknown whether there exists an intrinsic property responsible for this phenomenon. I'll describe a few examples demonstrating this phenomenon, one of which is a famous conjecture of Viterbo, and mention one intrinsic property that was recently shown to be not equivalent to convexity.