Title: Riemann-Hilbert correspondence, Fukaya categories and wall-crossing formulas
Speaker: Yan Soibelman
Speaker Info: Kansas State
Conventionally, the Riemann-Hilbert correspondence relates (at the derived level) the category of holonomic D-modules ("de Rham side") and the category of constructible sheaves ("Betti side"). It is natural to ask how should the RH-correspondence look like if we replace the algebra of differential operators by the quantized algebra of functions on a complex symplectic manifold more general than the cotangent bundle. I am going to explain that in general on the Betti side one should place an appropriate Fukaya category. A good example is the RH-correspondence for quantum tori (i.e. difference equations).Date: Thursday, March 23, 2017
Furthermore, one should consider the RH-correspondence in families (e.g. to formulate it not for an individual bundle with connection but for a bundle endowed with an h-connection, as the parameter h varies and can go to 0). In this way pseudo-holomorphic discs from the Floer theory and resurgence properties of the WKB solutions enter the story. The talk is based on the (part of the) project "Holomorphic Floer theory" joint with Maxim Kontsevich.