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# Geometric and Topological Recursion 

## General 

- [Survey paper](https://arxiv.org/pdf/1103.4674.pdf)
- ![](attachments/PhDthesis.pdf)
- [Defining the WP form](http://www2.math.umd.edu/~wmg/SymplecticNature.pdf)



## Topological and Geometric Recursion

- Good overview: <https://www.ams.org/books/pspum/100/pspum100-endmatter.pdf>
- MIRZAKHANI on Weil-Petersson volumes and intersection theory on $\MM_{g, n}$<https://www.ams.org/journals/jams/2007-20-01/S0894-0347-06-00526-1/S0894-0347-06-00526-1.pdf>
- Eynard's overview of topological recursion:  <https://arxiv.org/pdf/1412.3286.pdf>
- Mini-course on topological and geometric recursion: <https://arxiv.org/pdf/1705.09986.pdf>

# Definitions

:::{.definition title="Hermitian Metric"}
A **Hermitian metric** is a smoothly varying Hermitian inner product on tangent spaces, so $g(z, w) = \bar{g(w, z)}$, like the inner product on a Hilbert space over $\CC$.

  - More generally, for any $E\in \VectBundle\slice{\CC}$, a smooth section $\Gamma(E, \tensor \bar{E})\dual$.
  - Analog of self-adjointness, since for matrices $A$ is Hermitian iff $A = A^\dagger \da \bar{A^t}$.

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:::