Maxim Jeffs, Harvard University, Côme Dattin, University of Nantes,

Maxim Jeffs, Harvard University, Côme Dattin, University of Nantes,

Three 20 Minute Research Talks

Zoom link:

Maxim Jeffs, Harvard University,  Mirror symmetry and Fukaya categories of  singular varieties

In this talk I will explain Auroux' definition of the Fukaya category of a singular hypersurface and two results about this definition, illustrated with some examples. The first result is that Auroux' category is equivalent to the Fukaya-Seidel category of a Landau-Ginzburg model on a smooth variety; the second result is a   homological mirror symmetry equivalence at certain large complex   structure limits. I will also discuss ongoing work on generalizations.

Côme Dattin, University of Nantes, Wrapped sutured Legendrian homology and the conormal of braids

In this talk we will discuss invariants of sutured Legendrians. A sutured contact manifold can be seen as either generalizing the contactisation of a Liouville domain, or as a presentation of a contact manifold with convex boundary. Using the first point of view, we define the wrapped sutured homology of Legendrians with boundary, employing ideas coming from Floer theory. To illustrate the second aspect, we apply the unit conormal construction to braids with two strands, which yields a sutured Legendrian. We will show that, if the conormals of two 2-braids are Legendrian isotopic, then the braids are equivalent.

Bingyu Zhang Institut Fourier, Université Grenoble Alpes, Capacities from the Chiu-Tamarkin complex

In this talk, we will discuss the Chiu-Tamarkin complex. It is a symplectic/contact invariant that comes from the microlocal sheaf theory. I will explain how to define some capacities using the Chiu-Tamarkin complex in both symplectic and contact situations. The main result is the structure theorem of the Chiu-Tamarkin complex of convex toric domains. Consequently, we can compute the capacities of convex toric domains.