**201**

**11:00**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.

**14:15**Umberto Hryniewicz (Rio de Janeiro)

**Local subharmonic invariants of periodic points of Hamiltonian**

diffeomorphisms.

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.

**16:00**Laurent Charles (Paris 6 et ENS)

**TBA.**

*Abstract:*TBA.

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.