Speaker:  Yan Soibelman (Kansas State University)

Title:  Holomorphic Floer Theory and Chern-Simons theory.

Abstract:  Holomorphic Floer Theory (HFT) is the name of the project which we have been developing jointly with Maxim Kontsevich since 2014. This talk is based on several sections of the large file which we plan to publish in the future (probably in the form of several papers).

HFT studies questions of "Floer-theoretical nature" in the framework of complex symplectic manifolds. Similarly to the Homological Mirror Symmetry (HMS) there are "A-side" and "B-side" of HFT. But differently from the HMS in the HFT the equivalence of A and B sides relates categories associated to the SAME complex symplectic manifold. The equivalence has a form of the (generalized) Riemann-Hilbert correspondence.

In the first part of my talk I plan to review some basic ideas and examples of HFT. In the second part I am going to explain how these ideas lead to a conjectural approach to Chern-Simons theory. In particular I plan to discuss the corresponding Hodge structure of infinite rank as well as a conceptual reason for resurgence (Borel resummability) of perturbative expansions in the Chern-Simons theory.