Séminaire - Septembre
Le séminaire aura lieu un mercredi par mois de 14h à 15h à l'Institut Henri Poincaré à Paris. Pour télécharger l'affiche du mois: septembre.pdf.
- 07/09/2022 - Giovanni Forni (University of Maryland) - salle 01
Titre:
A Central Limit Theorem for the Kontsevich--Zorich cocycle
Resumé: The
Kontsevich--Zorich (KZ) cocycle is a key dynamical system closely
related to the tangent cocycle of
the Teichmueller geodesic flow. The main goal of the talk is to sketch
a proof of a Central Limit Theorem first for a version
of the KZ cocycle over the foliated Brownian motion on Teichmueller
disks, then for the usual deterministic KZ cocycle.
The above-mentioned CLT's are proved in great generality, but the
positivity of the variance for the deterministic KZ cocycle
is restricted by the hypothesis of simple Lyapunov spectrum. These
results were also originally motivated by the goal of proving the
existence of significant fluctuations of the Hodge norm of the parallel
transport of vectors along Teichmueller horocycles. These fluctuations
are behind recent results by Chaika, Khalil
and Smillie on ergodic measures of the Teichmueller horocycle flow. The
arguments are based on Hodge theory, potential theory and stochastic
calculus (hence they don't come from a general CLT
for cocycles over hyperbolic systems). Our work is joint with
H.~Al-Saqban.