24th January: Lorenzo La Porta

Title: Generalized theta operators 

Abstract: The study of the classical theta operator was key to Edixhoven's proof of the weight part of Serre's modularity conjecture. Since then, a lot of work has been devoted to extending the construction of this operator to other Shimura varieties, with an eye towards generalisations of Serre's conjecture. My goal is to present the construction of some generalised theta operators that seem to produce exactly the weight shifts that one would expect from a representation-theoretic viewpoint. I'll start with a gentle introduction to some of the ideas and history behind the classical case and then focus on the unitary case of signature (2, 1).