2021 - T2 - Symplectic topology, contact topology and interactions

Collection 2021 - T2 - Symplectic topology, contact topology and interactions

Organizer(s) Colin, Vincent ; Humilière, Vincent ; Massot, Patrick ; Niederkrüger, Klaus ; Oancea, Alexandru ; Vaugon, Anne

Date(s) 19/04/2021 - 16/07/2021

linked URL https://indico.math.cnrs.fr/event/5767/

00:00:00 / 00:00:00

35 45

A few properties of Besse contact manifolds.

By Marco Mazzucchelli

Joint work with Alberto Abbondandolo and Christian Lange.

A closed connected contact manifold is called Besse when all of its Reeb orbits are closed, and Zoll when furthermore all Reeb orbits have the same minimal period. In this talk, I will present a recollection of recent results/work in progress on the subject: - It is known that Besse contact 3-spheres are strictly contactomorphic to rational ellipsoids. In higher dimensions, the analogous statement is open. Nevertheless, I will show that at least those contact (2n-1)-spheres that are convex hypersurfaces in symplectic vector spaces still "resemble" a rational ellipsoid. This is joint work with Marco Radeschi. - Inspired by recent results on the systolic optimality of Zoll contact manifolds, I will show that Besse contact 3-manifolds are local maximizers of a suitable generalized systolic ratio.

Information about the video

Date of recording 28/05/2021
Date of publication 28/05/2021
Institution IHP
Language English
Audience Researchers
Format MP4

Domain(s)

Symplectic Geometry

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