# Geometry and Mathematical Physics Seminar 2012/2013

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