University of Birmingham > Talks@bham > Geometry and Mathematical Physics seminar > Topological Recursion, Hurwitz theory, and moduli spaces of curves

Topological Recursion, Hurwitz theory, and moduli spaces of curves

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If you have a question about this talk, please contact Timothy Magee.

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Topological recursion (TR) is a technique developed by Chekhov, Eynard and Orantin about ten/fifteen years ago, which computes invariants recursively from the given input data of a spectral curve, even in the case the spectral curve is not provided by a matrix model. Examples of these invariants include Mirzakhani’s volumes of moduli spaces of hyperbolic surfaces, Gromov-Witten invariants, Hurwitz numbers of several kinds, Tutte’s enumeration of maps, asymptotics of coloured Jones polynomials of knots, and more. In particular, Hurwitz theory provides a good set of enumerative geometric problems whose numbers are (in some cases still conjecturally) generated via TR for different explicit spectral curves. Interestingly enough, these numbers are always linked to the cohomology of the moduli spaces of curves, and at the same time with integrable hierarchies of type 2D Toda or KP, contributing to the understanding of the interaction between Geometry and Mathematical Physics.

This talk is part of the Geometry and Mathematical Physics seminar series.

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