Séance du 13 décembre

Lieu: IHP, salle 01.

ATTENTION: Suite à une annulation, le programme est légèrement modifié.

11:00 Peter Albers (Heidelberg)
Polygonal symplectic billiards.
Abstract: I will explain the definition and present basic properties of a billiard system which we call symplectic billiards. After the general part I will focus on the polygonal case and present several results and conjectures which are inspired by numerical experiments.

14:15 Roman Golovko (Prague)
On Legendrian products and twist spuns.
Abstract: The Legendrian product of two Legendrian knots, as defined by Lambert-Cole, is a Legendrian torus. We show that this Legendrian torus is a twist spun whenever one of the Legendrian knot components is sufficiently large. We then study examples of Legendrian products which are not Legendrian isotopic to twist spuns. In order to do this, we prove a few structural results on the bilinearised Legendrian contact homology and augmentation variety of a twist spun. In addition, we show that the threefold Bohr-Sommerfeld covers of the Clifford torus and Chekanov torus are not twist spuns. This is joint work with Georgios Dimitroglou Rizell.

Prochaines séances: 10 janvier (Giroux, Laudenbach, Buhovsky), 6 mars (Bertelson, De Groote, Florio), 3 avril (Fermé, ? , ?)

Autre activité symplectique à Paris:
Séminaire Nantes-Orsay

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