# Topological recursion and deformation quantization.

### APA

Soibelman, Y. (2016). Topological recursion and deformation quantization.. Perimeter Institute. https://pirsa.org/16120015

### MLA

Soibelman, Yan. Topological recursion and deformation quantization.. Perimeter Institute, Dec. 08, 2016, https://pirsa.org/16120015

### BibTex

@misc{ pirsa_16120015, doi = {10.48660/16120015}, url = {https://pirsa.org/16120015}, author = {Soibelman, Yan}, keywords = {Mathematical physics}, language = {en}, title = {Topological recursion and deformation quantization.}, publisher = {Perimeter Institute}, year = {2016}, month = {dec}, note = {PIRSA:16120015 see, \url{https://pirsa.org}} }

Yan Soibelman Kansas State University

## Abstract

About a decade ago Eynard and Orantin proposed a powerful computation algorithm

known as topological recursion. Starting with a ``spectral curve" and some ``initial data"

(roughly, meromorphic differentials of order one and two) the topological recursion produces by induction

a collection of symmetric meromorphic differentials on the spectral curves parametrized by

pairs of non-negative integers (g,n) (g should be thought of as a genus and n as the number of punctures).

Despite of many applications of the topological recursion (matrix integrals, WKB expansions, TFTs, etc.etc.)

the nature of the recursive relations was not understood.

Recently, in a joint work with Maxim Kontsevich we found a simple underlying structure of the recursive relations of Eynard and Orantin. We call it ``Airy structure". In this talk I am going to define this notion and explain how the recursive relations of Eynard and Orantin follow from the quantization of

a quadratic Lagrangian subvariety in a symplectic vector space.