University of Birmingham > Talks@bham > Geometry and Mathematical Physics seminar > Introduction to geometric recursion

Introduction to geometric recursion

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If you have a question about this talk, please contact Andrea Brini.

The geometric recursion is a general construction whose goal is to produce mapping class group invariant quantities by a glueing principle (reminiscent of quantum field theories) from a small amount of initial data. It also lifts the topological recursion of Eynard-Orantin (which is known to apply to many enumerative problems) to an intrinsically geometric setting. After motivating the underlying ideas with a few examples, I will present an instance of this construction taking values in continuous function on Teichmuller space. It is designed in a such a way that after integration over the moduli space of bordered Riemann surface, we obtain quantities satisfying the topological recursion. I will give three examples of initial data, respectively related to Mirzakhani identity and recursion for the Weil-Petersson volumes, to Witten-Kontsevich intersection numbers, and present a generalization of Mirzakhani identity showing that statistics of lengths of multicurves satisfy the geometric recursion. I will also show that for a variant of the construction the geometric recursion can produce the determinant of the Laplacian. This is joint work with Andersen and Orantin.

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

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