Symplectic capacities of convex bodies and geodesics in the space of contact forms

Speaker. Alberto Abbondandolo
Date. 24.10.23 at 14:30

Abstract. An old open question in symplectic geometry asks whether all normalised symplectic capacities coincide on convex bodies in the standard symplectic vector space. I will show that this question has a positive answer for smooth convex bodies which are C^2-close to a Euclidean ball. This is related to the question of existence of minimising geodesics in the space of contact forms on a closed contact manifold equipped with a Banach-Mazur-like metric. The talk is based on recent joint work with Gabriele Benedetti and Oliver Edtmair.