Robert Krzyzanowski : Modular curves as Riemann surfaces

Posted by , part of the Graduate Number Theory Seminar.

At

Feb. 9, 2009, 3 p.m.

In

SEO 427

Abstract

To each congruence subgroup $\Gamma$ of $SL_2(\mathbb{Z})$, we can associate a modular curve to be the quotient space $\Gamma/\mathbb{H}$ (where $\mathbb{H}$ is the complex upper half plane). We will see the set of orbits generated by the action of $\Gamma$ can be made into a Riemann surface, which can then be compactified.