Séance du 4 novembre 2016

Lieu: IHP, salle 201


11:00  Umberto Hryniewicz (Rio de Janeiro) 
Local subharmonic invariants of periodic points of Hamiltonian

Abstract: As is well-known, the variational structure underlying
Hamiltonian systems makes their fixed point theory richer than as
predicted by Lefschetz theory. In this talk I will explore the
variational structure of the discretized action functional to put on
rigorous grounds the existence of new local invariants of periodic
points of Hamiltonian diffeomorphisms. These invariants, which are of
a subharmonic nature, are different from local Floer homology. Their
existence was predicted in previous work as a local contact homology.
Our new point of view allows us to completely understand their
iteration properties by means of an "invariant shifting lemma". As a
byproduct of the methods we establish some transversality results in
Morse homology with finite cyclic group symmetries. This is joint work
with Hein and Macarini.

14:15  Florent Balacheff (Lille) 
Systolic contact geometry.
Abstract: Systolic geometry involves a lot of ingredients like algebraic topology, metric geometry or conformal techniques for instance. In this talk, after briefly recall part of this background, we will explain why contact geometry is a natural setting for the study of isosystolic inequalities and the new perspectives it offers. This is joined work with J.C. Alvarez Paiva and K. Tzanev.

16:00  Laurent Charles (Paris 6 et ENS) 
Quantum speed limit vs displacement energy.

Abstract: The quantum speed limit is a universal bound on the energy required to pass from one state to another orthogonal state in a quantum system. Similarly, in symplectic topology, the displacement energy is the minimal energy needed to displace a given subset of a symplectic manifold. I will discuss how these two notions are related in the semiclassical limit. Joint work with Leonid Polterovich.

Prochaines séances: 2 décembre (S. Suhr, S. Courte, ?), 6 janvier.

Autre activité symplectique à Paris:
- Séminaire Nantes-Orsay
- Soutenance de thèse Maÿlis Limouzineau: le 21 octobre à 14h à Jussieu.
- Doctorat Honoris Causa de Dusa McDuff : les 10 et 11 octobre à Paris 6.