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Seminars

This page shows Lecture Series session by session. To browse how they were grouped and any global information see Lecture Series.


Room P3.10, Mathematics Building

Nicolas Orantin, Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Instituto Superior Técnico
New developments in topological recursion

Since its introduction in the context of random matrix theory for the enumeration of maps, the topological recursion formalism mysteriously appeared as a common solution to a large class of problems of enumerative geometry. In particular, as many examples suggest, Gromov-Witten invariants enumerating holomorphic maps from a surface of given topology to a given ambient space seem to be computable by this formalism by induction on the Euler characteristic of the embedded surfaces. In these lectures I will show how localization computations allow, using some combinatorics, to reduce the computation of these Gromov-Witten invariants to a sum over graphs which can then be obtained by a local version of the topological recursion. I will first present a few explicit examples before explaining the general setup based on a theory developed by Givental.

Based on joint works with Dunin-Barkowski, Eynard, Shadrin and Spitz.