Oberseminar: Riemann surfaces and topological recursion

Inhalt:

Topological recursion is a new universal structure, which has been recently applied to different applications like the Kontsevich model and Mirzakhani's recursions codifying intersection numbers and volumes for moduli spaces of Riemann surfaces, as well as recursions in Hurwitz and Gromov-Witten theory. Starting from the initial data of a spectral curve, topological recursion constructs a hirachy of differential forms codifying these invariants. This seminar gives an introduction to these ideas for the Kontsevich model following the book "Counting surfaces" of B.Eynard. At the same time the needed background on the theory of Riemann-Surfaces will be introduced, like (ramified) coverings, uniformization, meromorphic (Strebel) differential forms and moduli spaces of Riemann surfaces and their Deligne-Mumford compactifications. Since this is a seminar for a transfer of knowledge, there will be time for additional questions and discussions.

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