Séance du 8 novembre 2013

Lieu : IHP, salle 421

11:00  Vera Vertesi (Nantes) :

    A knot Floer-homology-like TQFT for braids.

Résumé: Knot Floer homology is an invariant of knots, that in its simplest flavor associates a bigraded vectorspace to knots. The original definition of Ozsv\'ath and Szab\'o counts solutions of partial differential equations associated to the knot. Since then a completely combinatorial version was given by Manolescu, Ozsv\'ath and Sarkar, and Manolescu, Ozsv\'ath, Szab\'o and Thurston. In the talk I outline another combinatorial approach, by defining a Topological Quantum Field Theory for plat representations of open braids, which recovers knot Floer homology when closed up. The definition while completely combinatorial imitates the approach of bordered Floer homology. This is a joint work (in progress) with Ina Petkova

14:00  Jonny Evans (Londres) :

    Unlinking and unknottedness of monotone Lagrangian submanifolds
Résumé: I will explain some recent joint work with Georgios Dimitroglou Rizell in which we use moduli spaces of holomorphic discs with boundary on a monotone Lagrangian torus in $ {\mathbf C}^n $ to prove that all such tori are smoothly isotopic when n is odd and at least 5.

15:45  Baptiste Chantraine (Nantes) :

    Lagrangian Floer Theory for Lagrangian cobordisms.

Résumé: In this talk we will relates algebraic invariants of Legendrian sub-manifolds with algebraic invariants of Lagrangian cobordisms between them. Our construction generalises the construction of Lagrangian Floer homology (as described by T. Ekholm) for pairs of Lagrangian in the symplectisation of a contact manifolds with possibly non-empty concave cylindrical boundary. As an application we will describe a long exact sequence relating the bilinearised Legendrian contact homology of $L^+$ and $L^-$ and the singular homology of $S$ when $S$ is an exact Lagrangian cobordism from $L^-$ to $L^+$. If time permits we will describe application of this long exact sequence. As usual, all the preliminary definitions will be given. This a joint work with Georgios Dimitroglou Rizell, Paolo Ghiggini and Roman Golovko.

Prochaines séances: 6/12 (C. Wendl, A. Ritter, ?), 10/01 (?,?,?)