A Central Limit Theorem for the Kontsevich-Zorich cocycle
Vortrag von Dr. Hamid Al-Saqban
Sprecher eingeladen von: Prof. Dr. Artur Avila
Datum: 06.11.24 Zeit: 13.30 - 14.30 Raum: Y27H28
The Kontsevich-Zorich (KZ) cocycle is a key dynamical system that is closely related to the derivative cocycle of the Teichmüller geodesic flow. We will state and sketch a proof of a central limit theorem for the KZ cocycle, and explain some of the motivations, especially towards the goal of proving the existence of large fluctuations of the Hodge norm of the parallel transport of vectors along Teichmüller horocycles. Such fluctuations were leveraged by Chaika-Khalil-Smillie in their work on the ergodic measures of the Teichmüller horocycle flow. Our work is joint with Giovanni Forni.