Video URL
https://pirsa.org/16120015Topological recursion and deformation quantization.
APA
Soibelman, Y. (2016). Topological recursion and deformation quantization.. Perimeter Institute for Theoretical Physics. https://pirsa.org/16120015
MLA
Soibelman, Yan. Topological recursion and deformation quantization.. Perimeter Institute for Theoretical Physics, Dec. 08, 2016, https://pirsa.org/16120015
BibTex
@misc{ scivideos_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 for Theoretical Physics},
year = {2016},
month = {dec},
note = {PIRSA:16120015 see, \url{https://scivideos.org/index.php/pirsa/16120015}}
}
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.