Vincent Bouchard - An introduction to Airy structures from the point of view of D-modules - 16.06.23
Channel: Hörsaal Mathematikon
Date: 18/06/2023

Hodge theory, Mirror Symmetry, and Physics of Calabi-Yau Moduli
https://web.mathi.uni-heidelberg.de/cymod23
A MATCH-PIMS-STRUCTURES workshop in Mathematical Physics, held from June 12 to 16, 2023, at the Mathematikon in Heidelberg
For more talks visit https://www.youtube.com/playlist?list=PL57PsbjMibmQ37JSKzyxqvmIhyAfF1iFs

Abstract: Airy structures were introduced by Kontsevich and Soibelman in 2017 as an algebraic reformulation and extension of the Chekhov-Eynard-Orantin topological recursion, which appears in many contexts, from enumerative geometry to mathematical physics. In this talk I will introduce the concept of Airy structures as particular left ideals in the Rees Weyl algebra, such that the quotient of the algebra by the ideal is canonically isomorphic to a Rees polynomial module twisted by an automorphism of a simple type. This approach provides a clean reformulation of the theory in the language of D-modules, in which the foundational existence and uniqueness theorem of Kontsevich and Soibelman follows naturally. I will then mention some recent applications of the theory to enumerative geometry, VOAs and gauge theories, and discuss potential generalizations. My hope with this talk is to convey why I believe that the formalism of Airy structures (and topological recursion) should be in the toolbox of all geometers and mathematical physicists!