SEMINARIO DI SISTEMI DINAMICI (olomorfi e dintorni)
Sala Seminari del Centro di Ricerca Matematica Ennio De Giorgi Palazzo Puteano
----> Martedi' 1 febbraio alle ore 14.30 <---- Sala Conferenze, (palazzo Puteano)Il Dr. Artur Avila (CNRS, Parigi)
terra' un seminario di sistemi dinamici dal titolo
The Zorich-Kontsevich conjecture
ABSTRACT An abelian differential on a compact Riemann surface of genus $g \geq 2$ determines a translation structure, and in particular a flat metric (with singularities at the zeroes). Numerical experiments by Zorich on the asymptotic behavior in homology of a typical geodesic of a typical translation surface showed a hierarchy of polynomial deviations organized in a Lagrangian flag. The work of Zorich and Zorich-Kontsevich justified this phenomenon by conjectured simplicity of the first $g$ Lyapunov exponents of the Teichmuller flow on the moduli space of abelian differentials. Partial results by Zorich-Kontsevich and Giovanni Forni were obtained, in particular settling the conjecture in genus $g=2$. We will discuss joint work with Marcelo Viana, which provides a proof of the full conjecture.
Marco Abate Stefano Marmi
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