Séance du 2 décembre 2016

ATTENTION, lieu inhabituel: Jussieu, salle 15-25-502.

11:00  Erkao Bao (Nantes) 
Semi-global Kuranishi charts and contact homology .
Abstract: Contact homology was proposed and studied by Eliashberg, Givental and Hofer 16 years ago. It is a very powerful tool to distinguish different contact structures. However, the rigorous definition did not come out until last year. In this talk, we will first see that the naive definition does not work because the moduli spaces of J-holomorphic curves that we count to define the differential of contact homology are not transversally cut out.  In order to achieve transversality, we will use a simplified version of the Kuranishi perturbation theory, consisting of "semi-global Kuranishi charts". This is a joint work with Ko Honda.

14:15  Stefan Suhr (Hamburg)  
A Hamiltonian version of a result of Gromoll and Grove.
Abstract: Many problem on closed geodesics in Riemannian manifolds have a reformulation as a symplectic or contact geometric problem. A celebrated result in the theory of Riemannian metrics all of whose geodesics are closed is the theorem of Gromoll and Grove asserting that the geodesics of a Riemannian maetric on the 2-sphere all of whose geodesics are closed are simple closed. This implies especially that all geodesics have a common minimal period. I will explain how generalize this theorem to real Hamiltonian structures, which includes contact structures, on the 3-dimensional real projective space. As a corollary one obtains that for reversible Finsler metrics all geodesics have the same length if they areall closed.

16:00  Sylvain Courte (Grenoble) 
Generating functions and sheaves for Legendrian links in R^3 .

Abstract: To a (generic) one-parameter family of functions (f_x) on a manifold M we associate the graph of all critical values : this is the front projection of a Legendrian link L in R^3 and (f_x) is called
a generating function for L. Which Legendrian links admit a generating function ? How many up to equivalence? To deal with such questions it is natural to associate to a generating function a sheaf on R^2 microsupported on the Legendrian. We will discuss to what extent this is a bijective correspondence. This is joint work (in progress) with Vivek Shende.

Prochaines séances: 6 janvier (M. Limouzineau, ?, ?), 3 mars (B. Chantraine, ?, ?).

Autre activité symplectique à Paris:
- Séminaire Nantes-Orsay
- Soutenance d'HDR de Patrick Massot le 12 décembre à 14h, petit amphi du batiment 425, à Orsay.  

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.