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### Friday, January 27, 2017

 All day Conference - CAST - Contact and Symplectic Topology Jan 26, 2017 to Jan 28, 2017 read more Download the poster in pdf Nantes, from January 26th to January 28th Organization board: Baptiste Chantraine, Vincent Colin, Paolo Ghiggini Scientific board: Jean-François Barraud, Baptiste Chantraine, Kai Cieliebak, Tobias Ekholm

 Before 01 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Sylvan Jan 27, 2017 I'll define a "partially wrapped" Fukaya category associated to a Liouville domain with "stops", which are Liouville hypersurfaces of the boundary. This category is closely related to Legendrian contact homology [Ekholm--Lekili, 1701.01284]. I'll explain how certain functors between partially wrapped Fukaya categories, when they exist, can give strong constraints on the structure of Legendrian contact homology. This existence can in some cases be inferred from mirror symmetry, and in general it conjecturally follows from the existence of certain positive loops.     Vertesi Jan 27, 2017 Knot Floer homology is an invariant for knots and links defined by Ozsvath and Szabo and independently by Rasmussen. It has proven to be a powerful invariant e.g. in computing the genus of a knot, or determining whether a knot is fibered. In this talk I define a generalisation of knot Floer homology for tangles; Tangle Floer homology is an invariant of tangles in D^3, S^2xI or in S^3. Tangle Floer homology satisfies a gluing theorem and its version in S^3 gives back a stabilisation of knot Floer homology. Finally, I will discuss how to see tangle Floer homology as a categorification of the Reshetikhin-Turaev invariant for the Alexander polynomial.     Orantin Jan 27, 2017 Together with Bertrand Eynard, we developed a formalism allowing to compute the asymptotic expansion of a large class of matrix integrals when the matrix is very large. We later generalized this inductive formalism under the name topological recursion as an efficient way to solve many different problems related to enumerative geometry such as the computation of Gromov-Witten invariants of different manifolds, of the Weil-Petersson volume of moduli spaces of Riemann surfaces, of intersection numbers, Hurwitz numbers or sums over (plane-)partitions. It is also believed to generalize the volume conjecture by computing many knot invariants. Even if a full general and geometric understanding of this success is still missing, I will present in this talk a brief introduction of the original formalism and its applications as well as a new point of view recently pointed out by Kontsevich and Soibelman presenting it as a way to quantize quadratic Lagrangians by providing the full WKB expansion of the associated wave function.             Wand Jan 27, 2017 The modern development of contact geometry in 3 dimensions has seen several (due to Giroux, Wendl, Latschev and Wendl, Hutchings, and others) invariants of contact structures meant in some sense to measure non-(Stein/symplectic)-fillability of the structure. We will discuss a new approach which uses Heegaard Floer homology to define an invariant with a similar aim, but which has several desirable properties lacking in earlier approaches. Time permitting, we will discuss some examples and applications. This is joint with joint work with Kutluhan, Matic, and Van Horn-Morris.         Simone Jan 27, 2017 Let (W; L, L') be a monotone Lagrangian cobordism. In some cases, for example when the minimal Maslov number of W is big enough, the fundamental groups of L and L' give a lot of information about the topology of $W$. Motivated by this question, we study the fundamental group of W using two approaches: a geometric approach based on Barraud's construction of the Floer fundamental group and an algebraic approach using Floer homology with local coefficients. This talk is based on a joint work with Jean-François Barraud.