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Séance du 4 novembre 2016

Lieu: IHP, salle **201 **

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

diffeomorphisms.
*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.