Séminaire actuellement dans le cadre du trimestre IHP.
Pour plus d'info voir ici: https://indico.math.cnrs.fr/event/5767/
10h45 : Alberto Abbondandolo (Bochum)
Title : Bi-invariant Lorentz-Finsler structures on the linear symplectic group and contactomorphism group.
Abstract : It is well known that the linear symplectic group and the
contactomorphism group do not admit any bi-invariant metric which is
compatible with the Lie group topology. In this talk, I will discuss
two mutually related bi-invariant Lorentz-Finsler structures on these
groups. The talk is based on some work in progress with Gabriele
Benedetti and Leonid Polterovich.
13h45 : Marco Mazzucchelli (ENS Lyon)
Abstract : 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. This is joint work with Alberto Abbondandolo and Christian Lange.
