Holomorphic Floer theory and deformation quantization


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


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


          @misc{ pirsa_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


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.