### Canadian

Mathematical

Society

## Vincent Bouchard

##### University of Alberta

Vincent Bouchard is Professor in the Department of Mathematical and Statistical Sciences at University of Alberta. He obtained his D.Phil. in Mathematics from University of Oxford in 2005, as a Rhodes scholar. He held postdoctoral fellowships in University of Pennsylvania, Mathematical Science Research Institute in Berkeley, Perimeter Institute for Theoretical Physics in Waterloo, and Harvard University, before joining University of Alberta in 2009.

His research focuses on exploring new mathematical structures physically motivated by modern physics, which often give rise to unexpected connections between mathematical objects that appear a priori unrelated. He is also passionate about teaching and creating an active learning environment in the classroom. Outside of math, Vincent likes to apply the perseverance and grit required of research in mathematics to the pursuit of long-distance sports and mountain adventures.

### Abstract

##### Monday, December 4, 2023 | 11am - 12pm

### Airy structures: a new connection between geometry, algebra and physics

Modern physics involves beautiful and intricate mathematics, and entirely new mathematical structures often emerge from physical theories. An example of this is the concept of Airy structures, which was first introduced by Kontsevich and Soibelman in 2017 as an algebraic reformulation and extension of the Chekhov-Eynard-Orantin topological recursion. One can also think of Airy structures as a wide generalization of Witten's conjecture; as such, it provides a fascinating new connection between enumerative geometry, algebra and integrable systems. In this talk I will introduce the concept of Airy structures, mention some recent applications of the theory to enumerative geometry, vertex operator algebras and gauge theories, and discuss potential generalizations and open questions. 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, algebraists and mathematical physicists!