Symplectic capacities, Viterbo isoperimetric conjecture, ... - Marco Mazzucchelli

Mathematics Department Colloquium - May 9, 2024
Stony Brook University
Marco Mazzucchelli, École normale supérieure de Lyon
Title: Symplectic capacities, Viterbo isoperimetric conjecture, and contact manifolds all of whose Reeb orbits are closed
Abstract: Symplectic capacities are fundamental invariants that govern many rigidity phenomena in symplectic and contact topology. Their introduction in the 1980s by Ekeland and Hofer was motivated by the celebrated Gromov's non-squeezing theorem: a round ball in the symplectic vector space does not symplectically embed into a symplectic cylinder of smaller radius. A conjecture due to Viterbo from the early 2000s asserts that, among the 2n-dimensional convex bodies of volume one, the round balls are the ones with the largest capacity. In this colloquium talk, I will provide an informal and general overview of some developments in symplectic geometry related to the Viterbo conjecture, including its application to convex geometry, and the study of contact manifolds all of whose Reeb orbits are closed.