On Zorich's conjecture for hyperelliptic Rauzy monoids
speaker: Carlos Matheus Silva Santos ( CNRS)abstract: Rauzy monoids are combinatorial models for a renormalization scheme of interval exchange transformations and translation flows. In 2007, Avila and Viana solved the Kontsevich-Zorich conjecture on the simplicity of Lyapunov exponents of Rauzy monoids by showing certain pinching and twisting properties. An interesting feature of the techniques by Avila-Viana is that they establish simplicity of the Lyapunov spectrum without computing the Zariski closure of Rauzy monoids. In particular, as it is pointed out in their article, this solution of the Kontsevich-Zorich conjecture avoids the discussion of a conjecture of Zorich on the Zariski density of Rauzy monoids in symplectic groups. In this talk, we discuss a joint work with Avila and Yoccoz on the solution of Zorich's conjecture for hyperelliptic Rauzy monoids. Also, if the time permits, we will give some applications of our discussion to the non-continuity of neutral Oseledets subspaces andor to some conjectures of Ivanov and Putman-Wieland.
timetable:
Mon 4 Apr, 11:30 - 12:30, Aula Dini
<< Go back