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Realization of Veech groups for infinite translation surfaces

Anja Randecker

Heidelberg University (Alemania)

Abstract:

For this talk, we want to equip our surfaces (of finite or infinite type) additionally with a translation structure. This means that our surfaces can be obtained as gluings of Euclidean polygons. The symmetries of such translation surfaces are encoded in the subgroup of the mapping class group which preserves the translation structure. For surfaces of finite type, it is unknown which groups can be realized as symmetry groups whereas for surfaces of infinite type, much more is known already.

I will introduce translation surfaces and give an overview on known results on their symmetry groups, partly based on joint work in progress with Mauro Artigiani, Chandrika Sadanand, Ferrán Valdez, and Gabriela Weitze-Schmithuesen.