## Congruence properties of Veech groups

Gabriela Weitze
Universität des Saarlandes
Abstract:
Veech groups of translation surfaces are discrete subgroups of
$SL(2,\mathbb{R})$
. In the case of a special class of translation surfaces called origamis they are actually subgroups of
$SL(2,\mathbb{Z})$
of finite index. Congruence subgroups of
$SL(2,\mathbb{Z})$
are groups which are fully determined by their image in
$SL(2,\mathbb{Z}/n\mathbb{Z})$
for some
$n$
. We study Veech groups which are as far as possible from being a congruence group.