Maxim Jeffs, Harvard University, Côme Dattin, University of Nantes,
Maxim Jeffs, Harvard University, Côme Dattin, University of Nantes,
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Maxim Jeffs,ÌýHarvard University,ÌýÌýMirror symmetry and Fukaya categories ofÌý singular varieties
In this talk I will explain Auroux' definition of the FukayaÌýcategory of a singular hypersurface and two results about thisÌýdefinition, illustrated with some examples. The first result is thatÌýAuroux' category is equivalent to the Fukaya-Seidel category of aÌýLandau-Ginzburg model on a smooth variety; the second result is aÌý Ìýhomological mirror symmetry equivalence at certain large complexÌý Ìýstructure limits. I will also discuss ongoing work on generalizations.
Côme Dattin, University of Nantes,ÌýWrapped sutured Legendrian homology and theÌýconormal of braids
In this talk we will discuss invariants of suturedÌýLegendrians. A sutured contact manifold can be seen as eitherÌýgeneralizing the contactisation of a Liouville domain, or as aÌýpresentation of a contact manifold with convex boundary. Using theÌýfirst point of view, we define the wrapped sutured homology ofÌýLegendrians with boundary, employing ideas coming from Floer theory.ÌýTo illustrate the second aspect, we apply the unit conormalÌýconstruction to braids with two strands, which yields a suturedÌýLegendrian. We will show that, if the conormals of two 2-braids areÌýLegendrian isotopic, then the braids are equivalent.
Bingyu Zhang Institut Fourier, Université Grenoble Alpes,ÌýCapacities from the Chiu-Tamarkin complex
In this talk, we will discuss the Chiu-Tamarkin complex. ItÌýis a symplectic/contact invariant that comes from the microlocal sheafÌýtheory. I will explain how to define some capacities using theÌýChiu-Tamarkin complex in both symplectic and contact situations. TheÌýmain result is the structure theorem of the Chiu-Tamarkin complex ofÌýconvex toric domains. Consequently, we can compute the capacities ofÌýconvex toric domains.