WiSe 2019/20 Zeit: Mittwoch, 16:00 – 18:00 Uhr Ort: M6 Veranstalter: Lutz Hille, Helmut Hamm, Jörg Schürmann, Raimar Wulkenhaar 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. Vorträge: Oberseminar: Riemann surfaces and topological recursion
Datum
Sprecher
Titel
30.10.2019
Raimar Wulkenhaar
The Bochner-Minlos Theorem
06.11.2019
Jörg Schürmann
Introduction to Riemann surfaces
20.11.2019
Alexander Hock
Maps of discrete surfaces and Tutte's equations
27.11.2019
Johnannes Branahl
Duality between ribbon graphs and maps of discrete surfaces
11.12.2019
Jörg Schürmann
Introduction to Riemann surfaces, part II
19.12.2019
Jörg Schürmann
Introduction to holomorphic vector bundles
15.01.2020
Jörg Schürmann
Chern classes of holomorphic line bundles