Symplectic Capacities, Viterbo Isoperimetric Conjecture, and Contact Manifolds with Closed Reeb Orbits

Explore the fundamental concepts of symplectic geometry in this Mathematics Department Colloquium talk by Marco Mazzucchelli from École normale supérieure de Lyon. Delve into the world of symplectic capacities, crucial invariants that govern rigidity phenomena in symplectic and contact topology. Trace the origins of these concepts to Ekeland and Hofer's work in the 1980s, inspired by Gromov's non-squeezing theorem. Examine Viterbo's conjecture from the early 2000s, which posits that round balls have the largest capacity among 2n-dimensional convex bodies of volume one. Gain insights into recent developments in symplectic geometry related to the Viterbo conjecture, including its applications in convex geometry. Explore the fascinating study of contact manifolds where all Reeb orbits are closed. This comprehensive overview offers a blend of historical context, theoretical foundations, and cutting-edge research in the field of symplectic geometry.