CRM: Centro De Giorgi
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Regular and Stochastic Behaviour in Dynamical Systems

Symplectic capacities of domains close to the ball and quasi-invariant contact forms

speaker: Alberto Abbondandolo (Ruhr Universität Bochum)

abstract: An old open question in symplectic dynamics asks whether all normalized symplectic capacities coincide on convex domains. I will discuss this question and show that the answer is positive if we restrict the attention to domains which are close enough to a ball. The proof is based on a “quasi-invariant” normal form in Reeb dynamics, which has also implications about geodesics in the space of contact forms equipped with a Banach-Mazur pseudo-metric. This talk is based on a joined work with Gabriele Benedetti and Oliver Edtmair.

Mon 5 Jun, 11:30 - 12:30, Aula Dini
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