Riemann-Hilbert correspondence revisited

Homological Mirror Symmetry Seminar
Topic:Riemann-Hilbert correspondence revisited
Speaker:Yan Soibelman
Affiliation:Kansas State University
Date:Wednesday, November 2
Time/Room:10:45am - 12:00pm/West Building Lecture Hall
Video Link:https://video.ias.edu/homologicsym/2016/1102-YanSoibelman

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.