Ober­se­mi­nar "Geo­me­tri­sche Ana­ly­sis und Zah­len­the­o­rie": Ha­mid Al Saq­ban -- hy­brid

Veranstalter: D 1 320

Title: Limit theorems and the Kontsevich-Zorich cocycle

Abstract: The Kontsevich-Zorich (KZ) cocycle is a dynamical system that is closely related to the derivative cocycle of the Teichmuller geodesic flow. While these dynamical systems are interesting in and of themselves, they also act as renormalizing dynamical systems for straight-line flows on translation surfaces. The main goal of these two talks is to introduce and motivate translation surfaces and their moduli spaces, and to state and sketch the proofs of recent results, parts of which are joint with G. Forni, that establish the existence of large fluctuations for the asymptotic growth of the norm of the KZ cocycle.