Rodolfo Gutierrez

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.