Veech groups of infinite translation surfaces

The Veech group of a translation surface is a discrete subgroup of
SL(2,R) which encodes a lot of information about the dynamics on the
translation surface. Particular explicit examples are provided by origamis
or square tiled surfaces for which the Veech group is always a subgroup of
SL(2,Z) and can be described in an alternative way using subgroups of the
automorphism group of F_2.
We study an infinite family of infinite volume origamis. They come from
coverings of the torus of infinite degree; these translation surfaces are
not of finite type. We show that their Veech groups are not finitely
generated. This is joint work with Pascal Hubert.