Séminaire - Mai
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: mai.pdf.
- 10/05/2023 - Simion Filip (University of Chicago) - salle 05
Titre: Lyapunov exponents, Anosov representations, and Hodge theory
Resumé: Lyapunov
exponents are in general not easy to compute or even estimate.
Nonetheless, using tools from Hodge theory it is possible to give lower
bounds, and even formulas, in some cases. I will discuss the proof of
one such formula for Lyapunov exponents conjectured by Eskin,
Kontsevich, Moller, and Zorich. The proof also gives the Anosov
property of associated monodromy representations, or equivalently that
of domination for certain cocycles. This in turn has many further
geometric consequences including Torelli theorems for certain families
of Calabi-Yau manifolds and uniformization results for domains of
discontinuity of the associated discrete groups. The necessary context
and background will be explained.