Topological recursion and deformation quantization.


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


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


          @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


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.