A Few Properties of Besse Contact Manifolds

Explore the intricacies of Besse contact manifolds in this comprehensive lecture by Marco Mazzucchelli from CNRS & ENS de Lyon. Delve into recent findings and ongoing research in the field, including joint work with Alberto Abbondandolo and Christian Lange. Examine the known properties of Besse contact 3-spheres and their strict contactomorphism to rational ellipsoids. Investigate the open question of analogous statements in higher dimensions, focusing on contact (2n-1)-spheres as convex hypersurfaces in symplectic vector spaces. Learn about the resemblance of these higher-dimensional structures to rational ellipsoids, based on joint work with Marco Radeschi. Discover the local maximizer properties of Besse contact 3-manifolds in relation to a generalized systolic ratio, inspired by recent results on the systolic optimality of Zoll contact manifolds.