Séance du 8 novembre 2019

Lieu: IHP, salle 201.

11:00 Mélanie Theillière (Lyon)
Corrugation Process and Isometric Totally Real maps.
Abstract: In this talk, I will present a theorem for C1-isometric totally real embedding inspired from the Nash-Kuiper Theorem for C1-isometric embeddings. Moreover we will also see a property of C1-fractality for isometric totally real embeddings built previously. To prove the theorem for totally real, we will first give an overview of the proof of the Nash-Kuiper theorem. Then we will give details on a different way to complete the main step of the Nash-Kuiper Theorem using a Corrugation Process. The use of this process will allows to state the theorem in the totally real case. Moreover this process also allows to prove a C1-fractal behavior of the Maslov component of the isometric totally real embedding just built..

14:15 Damien Galant (Orsay)
Effective computation of the bilinearized Legendrian contact homology.
Abstract: We recall the definition of Legendrian knots in (R³ , ξ std) and the basic tools to study them. We define the contact homology of such Legendrian knots. We explain linerization processes which allow to extract information from the infinite-dimensional contact homology algebra. Augmentations are auxiliary objects needed for linerization. They turn out to be natural and interesting objects by themselves and we discuss a notion of equivalence of augmentations. We then introduce bilinearized Legendrian contact homology (BLCH), a generalisation of Legendrian contact homology introduced by Bourgeois and Chantraine. The first goal of the talk is to introduce combinatorial methods for the effective computation of BLCH which can be implemented informatically. We then discuss theoretical results obtained by these computational means. The second goal of the talk is to explain why BLCH is a complete invariant for the equivalence of augmentations.

16:00 Daniel Rosen (Bochum).
Titre: Geometries on groups of symplectic and contact transformations.
Abstract: The geometry of transformation groups is a central object of study in symplectic and contact geometry. In the former, the Hamiltonian group carries the famous Hofer norm, a canonical conjugation-invariant Finsler norm. In the latter, by contrast, the contactomorphism group admits no such Finsler norms, however recently many examples of norms have been discovered. In this talk we will survey recent results about the geometries of these two groups, with an emphasis on large-scale questions.

Prochaines séances: 13 décembre (Albers, Golovko, Salchow), 10 janvier

Autre activité symplectique à Paris:
Séminaire Nantes-Orsay

Séance du 4 octobre 2019

Lieu: IHP, salle 201.

11:00 Slava Pimenov (Jussieu)
Bornological Manifolds and bounded group cohomology.
Abstract: We are interested in properties of the comparison map between bounded continuous cohomology and (unbounded) continuous cohomology of a topological group G, in particular whether it is an isomorphism. While in discreet case the question has been mostly settled, even for semisimple Lie groups very little is known. The term bornology formalizes idea of boundedness, similar to how topology does it for continuity. It is used extensively in functional analysis to study bounded linear operators. We propose a notion of bornological manifolds that may provide a framework that allows us to put geometric group properties, topological dynamics and analytic properties of topological vector spaces together, and use sheaf-theoretic methods to address this question. This is a joint work with Kobi Kremnitzer..

14:15 Jean-Paul Mohsen (Marseille)
Construction de sous-variétés complexes à courbure négative.
Abstract: Le premier but des techniques asymptotiques de Donaldson-Auroux était de transposer dans le cadre général de la géométrie symplectique certains résultats classiques de géométrie projective. Néanmoins, Donaldson avait noté que ces techniques avaient aussi des applications dans le cadre projectif. On présentera de nouveaux exemples de telles applications.

16:00 Yusuke Kawamoto (ENS).
Titre: C0 continuity of the spectral norm on non-symplectically aspherical manifolds.
Abstract: I will discuss the C0 continuity of the spectral norm on the group of Hamiltonian diffeomorphisms for some non-symplectically aspherical manifolds. The method is based on a recent work of Buhovski-Humiliere-Seyfaddini where they prove the continuity in the case of symplectically aspherical manifolds. In this talk, I focus to explain how to push their method to the non-symplectically aspherical case.

Prochaines séances: 8 novembre (Rosen, Theillière, Galant), 13 décembre (Albers, Golovko, Salchow), 10 janvier

Autre activité symplectique à Paris:
Séminaire Nantes-Orsay