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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 and Number Theory seminar series.

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