Airy structures: from algebra to geometry via representation theory

Abstract: Airy structures (introduced by Kontsevich and Soibelman) are systems of compatible PDEs admitting a unique (when suitably normalized) solution. This solution can be reconstructed by a topological recursion, i.e. a recursion that mimic cut-and-paste relations in the geometry of surfaces. There are in fact many examples of Airy structures where the solution encode enumeration of surfaces. Airy structure can be notably found from free field representations of certain vertex operator algebras, in particular from W-algebras. It can also be used to construct Whittaker vectors that are of interest in supersymmetric gauge theories. The talk will be an introduction to algebraic aspects of Airy structures, placed in the context of applications to geometry.

This is based on joint works with Andersen, Chekhov, Orantin, Bouchard, Creutzig, Chidambaram, Noschenko, Kramer, Schüler.

mathematical physicscombinatoricsgroup theoryrings and algebrasrepresentation theory

Audience: researchers in the topic

( video )

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Seminario de álgebra, combinatoria y teoría de Lie

Series comments: The talks are usually in Spanish. Las instrucciones para recibir el link de zoom están en la página web del seminario: sites.google.com/view/semact-uns/.

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