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Les Houches lecture notes on topological recursion
by Vincent Bouchard
Submission summary
| Authors (as registered SciPost users): | Vincent Bouchard |
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| Preprint Link: | https://arxiv.org/abs/2409.06657v1 (pdf) |
| Date submitted: | Oct. 9, 2025, 7:10 p.m. |
| Submitted by: | Vincent Bouchard |
| Submitted to: | SciPost Physics Lecture Notes |
| for consideration in Collection: |
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| Academic field: | Physics |
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| Approach: | Theoretical |
Abstract
You may have seen the words "topological recursion" mentioned in papers on matrix models, Hurwitz theory, Gromov-Witten theory, topological string theory, knot theory, topological field theory, JT gravity, cohomological field theory, free probability theory, gauge theories, to name a few. The goal of these lecture notes is certainly not to explain all these applications of the topological recursion framework. Rather, the intention is to provide a down-to-earth (and hopefully accessible) introduction to topological recursion itself, so that when you see these words mentioned, you can understand what it is all about. These lecture notes accompanied a series of lectures at the Les Houches school "Quantum Geometry (Mathematical Methods for Gravity, Gauge Theories and Non-Perturbative Physics)" in Summer 2024.