Examples around the strong Viterbo conjecture

Abstract: The Viterbo conjecture states that the ball maximizes any normalized symplectic capacity within all convex sets in R^{2n} of a fixed volume and that it is the unique maximizer. A stronger conjecture says that all normalized capacities coincide for convex sets. In joint work with Gutt and Hutchings, we prove the stronger conjecture for a somewhat different class of 4-dimensional domains, namely toric domains with a dynamically convex toric boundary. In joint work with Ostrover and Sepe, we prove that a 4-dimensional Lagrangian product which is a maximizer of the Hofer-Zehnder capacity is non-trivially symplectomorphic to a ball giving further evidence to the uniqueness claim of Viterbo's conjecture. In this talk, I will explain the proof of these two results.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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