# Lecture notes on topological recursion and geometry

@article{Borot2017LectureNO, title={Lecture notes on topological recursion and geometry}, author={Gaetan Borot}, journal={arXiv: Mathematical Physics}, year={2017} }

These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of topological recursion: in two dimensional quantum field theories, in cohomological field theories, in the computation of Weil-Petersson volumes of the moduli space of curves; (b) relate them more specifically to Eynard-Orantin topological recursion (revisited…

## 15 Citations

Quantization of hyper-elliptic curves from isomonodromic systems and topological recursion

- MathematicsJournal of Geometry and Physics
- 2021

An invitation to 2D TQFT and quantization of Hitchin spectral curves

- Mathematics
- 2017

This article consists of two parts. In Part 1, we present a formulation of two-dimensional topological quantum field theories in terms of a functor from a category of Ribbon graphs to the endofuntor…

Topological recursion for Masur-Veech volumes.

- Mathematics
- 2019

We study the Masur--Veech volumes $MV_{g,n}$ of the principal stratum of the moduli space of quadratic differentials of unit area on curves of genus $g$ with $n$ punctures. We show that the volumes…

Derived deformation theory of algebraic structures

- Mathematics
- 2020

The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of…

Topological Recursion for Generalized $bc$-Motzkin Numbers

- Mathematics
- 2021

We present a higher genus generalization of bc-Motzkin numbers, which are themselves a generalization of Catalan numbers, and we derive a recursive formula which can be used to calculate them.…

Analyticity of the free energy for quantum Airy structures

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020

It is shown that the free energy associated to a finite-dimensional Airy structure is an analytic function at each finite order of the -expansion. Its terms are interpreted as objects living on the…

Isomonodromic deformations of a rational differential system and reconstruction with the topological recursion: The sl2 case

- Mathematics
- 2020

In this paper, we show that it is always possible to deform a differential equation ∂xΨ(x) = L(x)Ψ(x) with L(x)∈sl2(C)(x) by introducing a small formal parameter ℏ in such a way that it satisfies the…

A New Class of Higher Quantum Airy Structures as Modules of $\mathcal{W}(\mathfrak{gl}_r)$-Algebras

- Mathematics
- 2020

Quantum $r$-Airy structures can be constructed as modules of $\mathcal{W}(\mathfrak{gl}_r)$-algebras via restriction of twisted modules for the underlying Heisenberg algebra. In this paper we…

Geometric recursion

- Mathematics
- 2017

We propose a general theory to construct functorial assignments $\Sigma \longmapsto \Omega_{\Sigma} \in E(\Sigma)$ for a large class of functors $E$ from a certain category of bordered surfaces to a…

Super Quantum Airy Structures

- Mathematics, PhysicsCommunications in mathematical physics
- 2020

It is proved that to a given super quantum Airy structure one can assign a unique set of free energies, which satisfy a supersymmetric generalization of the topological recursion.

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