Thar she blows  in pursuit of a classification of finite index subgroups of SL_2(Z) in terms of wallpaper groups
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If you have a question about this talk, please contact Jonathan Nelson.
There is an equivariant map from the upper half plane (with SL_2(Z) acting by mobius transformations) to the complex plane (with the action of a subgroup affine transformations which preserve a triangular lattice). The homomorphism from SL_2(Z) onto this group of affine transformations provides an obvious source of finite index subgroups of SL_2(Z). The conjecture is that finite index subgroups are all “lifts” of subgroups of the translation subgroup. I will describe why the equivariant map is plausible, and talk about the kernel of the homorphism and the lifts of translation groups.
This talk is part of the Junior Algebra/Logic/Number Theory seminar series.
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