Holomorphic Floer theory and deformation quantization

Abstract: In his 21st problem Hilbert asked about reconstruction of Fuchsian differential equation from its monodromy. This Riemann-Hilbert problem has a long history of solutions and counterexamples. During last decades it was generalized in two different directions. Most well-known is the generalization to higher dimensions and D-modules, with possibly irregular singularities. The monodromy data are replaced by constructble sheaves. Another, less known, generalization deals with not necessarily differential equations, e.g. with difference of q-difference ones.

In 2014 together with Maxim Kontsevich we started a project on what we called Holomorphic Floer theory. The word "holomorphic" refers to the fact that we consider Floer theory (e.g. Fukaya categories) for comlex symplectic manifolds. Aim of my talk is to explain some parts of the project which lead to a general formulation of the Riemann-Hilbert correspondence as a relation between Floer theory and deformation quantization.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar