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Abstract |
The Lyapunov exponents have turned out to be a fundamental tool to understand SL(2, R) action on Teichmüller spaces. Anton Zorich and Maxim Kontsevich introduced these exponents in the 90's for any SL(2, R)-invariant submanifold in the Teichmüller space. Latter a link with variation of Hodge structure was pointed out by a theorem of Kontsevich and Forni, which states that the sum of these exponents is also the integral over the invariant locus of the curvature of the Hodge bundle. Thus we have a direct link between dynamical invariants (Lyapunov exponents) and algebraic geometry invariants (degree and euler caracteristic). More recently, Fei Yu has conjectured an even deeper bound between Lyapunov exponents and algebraic structure of the Hodge bundle through the Harder-Narasimhan filtrations.
In my talk I will first introduce some background about these exponents, and explain in a second time to which extend we hope these exponents to be a new powerful geometric invariant in algebraic geometry, based on recent work of Kappes and M?ller who showed non-commensurability of Deligne-Mostow non -arithmetic lattices ; and on some conjectures Kontsevich exposed recently at IHP in Paris. |
