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Speaker:
Gabriela Weitze-Schmithüsen
Zugehörigkeit:
KIT
Datum:
Don, 04/12/2014 - 16:30 - 17:30
Location:
MPIM Lecture Hall
Parent event:
Oberseminar Differentialgeometrie Teichmüller curves are algebraic curves in moduli space which are images of Teichmüller disks, i.e. of isometrically and holomorphically embedded Poincaré disks in Teichmüller space. A particularly handy class of Teichmüller curves comes from so-called origamis (or square-tiled surfaces). One starts with finitely many copies of the unit square in the Euclidean plane and glues them along their boundary according to a few combinatorial rules, such that one obtains a surface which is endowed with a holomorphic differential or equivalently with a translation structure. Teichmüller curves are up to birationality determined by an associated discrete subgroup of SL(2,R) called the Veech group. For origamis this is a subgroup of SL(2,Z) of finite index. We study for origamis in strata of low genus how far they are away from being congruence groups.
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