# Holomorphic Floer theory and deformation quantization

### APA

Soibelman, Y. (2020). Holomorphic Floer theory and deformation quantization. Perimeter Institute. https://pirsa.org/20030113

### MLA

Soibelman, Yan. Holomorphic Floer theory and deformation quantization. Perimeter Institute, Mar. 19, 2020, https://pirsa.org/20030113

### BibTex

@misc{ pirsa_20030113, doi = {10.48660/20030113}, url = {https://pirsa.org/20030113}, author = {Soibelman, Yan}, keywords = {Mathematical physics}, language = {en}, title = {Holomorphic Floer theory and deformation quantization}, publisher = {Perimeter Institute}, year = {2020}, month = {mar}, note = {PIRSA:20030113 see, \url{https://pirsa.org}} }

Yan Soibelman Kansas State University

## Abstract

Geometry of a pair of complex Lagrangian submanifolds of a complex symplectic manifold appears in many areas of mathematics and physics, including exponential integrals in finite and infinite dimensions, wall-crossing formulas in 2d and 4d, representation theory, resurgence of WKB series and so on.

In 2014 we started a joint project with Maxim Kontsevich which we named "Holomorphic Floer Theory" (HFT for short) in order to study all these (and other) phenomena as a part of a bigger picture.

Aim of my talk is to discuss aspects of HFT related to deformation quantization of complex symplectic manifolds, including the conjectural Riemann-Hilbert correspondence. Although some parts of this story have been already reported elsewhere, the topic has many ramifications which have not been discussed earlier.