For any 2-generated finite group G, we will consider G-Galois covers of elliptic curves E, ramified only above the identity. When G is abelian, such "G-structures" are equivalent to classical congruence level structures. When G is sufficiently nonabelian, the moduli spaces of elliptic curves with G-structures are noncongruence modular curves. From here, a theorem of Asada implies that every noncongruence modular curve arises as a component of such a moduli space for a suitable G. As time permits, we will describe connections with the Inverse Galois Problem, and the arithmetic of noncongruence modular forms.

### Algebra Seminar

Monday, January 23, 2017 - 3:15pm

#### Will Chen

Institute for Advanced Study