Lieu: IHP, amphi Darboux.
11:00 Steven Sivek (Imperial College)
Representations and sheaves for Legendrian knots
Abstract: We describe an A_\infty category built out of n-dimensional representations of the Chekanov-Eliashberg DGA of a Legendrian knot in R^3. The case n=1 recovers the augmentation category, which is known to be equivalent to a category of constructible sheaves of microlocal rank 1 constructed by Shende-Treumann-Zaslow. In this talk, we will discuss some evidence for the conjecture that the categories of n-dimensional representations and of microlocal rank n sheaves are equivalent for all n>1 as well. This is joint work with Baptiste Chantraine and Lenny Ng.
14:15 Cheuk Yu Mak(Cambridge)
Tropically constructed Lagrangians in mirror quintic threefolds
Abstract: In this talk, we will explain how to construct embedded closed Lagrangian submanifolds in mirror quintic threefolds using tropical curves and the toric degeneration technique. As an example, we will illustrate the construction for tropical curves that contribute to the Gromov–Witten invariant of the line class of the quintic threefold. The construction will in turn provide many homologous and non-Hamiltonian isotopic Lagrangian rational homology spheres, and a geometric interpretation of the multiplicity of a tropical curve as the weight of a Lagrangian. This is a joint work with Helge Ruddat.
16:00 Nassima Keddari (Strasbourg)
Lagrangian submanifolds and displaceability.
Abstract: The starting point of the talk is one result of M.Damian (2012) who proved a version of Audin’s conjecture for some displaceable monotone Lagrangian submanifolds. To do so, he defines a lifted version of Floer homology and the crucial argument is that this homology is zero for a displaceable Lagrangian.
Not all monotone Lagrangians are displaceable, but there are some which are “almost displaceable” in the sense that they have a neighbourhood where all other Lagrangians are displaceable (for example, a great circle in the sphere). Let L_0 be one of them, this means that if we choose a Lagrangian, L, “close” to L_0, it has the same topology and is displaceable. Therefore, the idea is to apply the proof of M.Damian to this Lagrangian and then deduce the same properties for L_0. However, to do so, we need to define Floer homology and its lifted version for L, which is not monotone. We will explain these constructions and give some other consequences arising from them.
Prochaines séances: 15/03 (Albers, Lin, Ritter), 12/04 (Benedetti, Meschler, Golovko), 10/05 (Dahinden, Nonenmacher, Salamon), 14/06 (Macarini,? , ?).
Autre activité symplectique à Paris:
Séminaire Nantes-Orsay
