Riemann-Hilbert correspondence revisited

Riemann-Hilbert correspondence revisited - Yan Soibelman

Yan Soibelman
Kansas State University
November 2, 2016
Conventional Riemann-Hilbert correspondence relates the category of holonomic $D$-modules (de Rham side) with the category of constructible sheaves (Betti side). I am going to reconsider this relationship from the point of view of deformation quantization (on the de Rham side) and Fukaya categories (on the Betti side). Besides of useful re-interpretations of some classical results (e.g. Deligne-Malgrange Riemann-Hilbert correspondence for irregular connections on curves), this point of view allows us to conjecture some new results, e.g.the Riemann-Hilbert correspondence for difference equations (e.g. quantum spectral curves). Contents of the talk is a part of a bigger project called "Holomorphic Floer theory", joint with Maxim Kontsevich.