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.