École polytechnique – Centre de Mathématiques Laurent Schwartz

10h30-12h00 – Rodolfo Gutierrez (Université du Chili)

"Rauzy-Veech groups of flat surfaces"

Abstract: The Teichmüller flow is a natural geodesic flow on the space of flat surfaces and the Rauzy–Veech algorithm is a way to track the changes in the geometry produced by this flow. Rauzy–Veech groups are the subgroups of Sp(2g, Z) arising from the homological action of such changes in the geometry. The larger they are, the richer is the dynamics produced by the Teichmüller flow.  In this talk, we will present a full classification of Rauzy–Veech groups for all connected components of strata of Abelian differentials, showing that they are the largest possible groups predicted by the monodromy constraints. In particular, they are arithmetic subgroups of Sp(2g, R). Moreover, we will show that some of these techniques can be extended to certain connected components of strata of quadratic differentials, showing that they Rauzy–Veech groups are also arithmetic.