# Geometry and Mathematical Physics Seminar 2012/2013

Thursday November 29: The Frank Adams Room (Room 1.212), the Alan Turing Building. 4pm

## Interpretations of the Eisenstein Series $E_2$ and Invariant Differential Operators Adam Biggs (University of Manchester)

adam.biggs-2@postgrad.manchester.ac.uk

We shall give an interpretation of the second Eisenstein series $E_2$ as defining a unique ${\mathop{SL}}_2(\mathbb Z)$-invariant differential operator and as a connection on the space $\Omega^{1,0}$ of holomorphic forms on $H$. We shall then explore some simple consequences of this identification and study similar differential operators for congruence subgroups.