Les structures de contact et leurs cousines symplectiques permettent de jeter des ponts entre topologie et systèmes dynamiques.
– Recherche d’orbites périodiques de champs de vecteurs ;
– Étude des espaces de courbes holomorphes ;
– Liens avec la théorie des noeuds.
On présentera quelques enjeux et méthodes de la géométrie de contact.

L'affiche

Le but de cet exposé est de donner quelques idées sur la collision de solitons contre un potentiel non linéaire, et pouvoir quantifier le défaut d'élasticité après la collision.

I will discuss a symplectic embedding problem for polydisks in dimension 4. Symplectic embeddings are a key phenomenon of symplectic rigidity. In the case I consider, the obstruction for embedding the polydisk comes from a certain Lagrangian torus and uses the theory of J-holomorphic foliations in dimension 4. This is joint work with Richard Hind.

A categorical group is a monoidal category with associator, left-right unitor are identity. Thus under the tensor product, both object and morphism sets are groups. Categorical groups have an equivalent description in terms of "crossed-modules". We will discuss the representations of categorical groups on "certain categorical spaces" and some of the consequences. We will introduce the notion of semi-direct product of categories and show how this notion can be used to give a more general description of representations of categorical groups. This is a joint work with A. Lahiri, A. N. Sengupta.

Is it possible to find an embedded Lagrangian disk in \C^n - B^2n, so that the boundary is a Legendrian in S^{2n-1}? When n=2 the answer is no, but in all higher dimensions such disks exist in abundance. This follows from a more general existence theorem for Lagrangian embeddings with loose concave boundary; in this two-part talk we precisely state and prove this theorem. The proof has two main components: an action-balancing lemma for Lagrangian immersions, and a Lagrangian Whitney trick. We discuss the proof of both, in particular discussing how they both rely on the classification theorem for loose Legendrians. This project is joint work with Yakov Eliashberg.