Differential operators on modular forms

Abstract: 

Rankin-Cohen brackets are a way of differentiating a modular form while preserving the modularity property.  This produces a differential operator on modular forms (mod p), whose effect on the attached Galois representations is tensoring by the cyclotomic character modulo p.

I will discuss how these ideas come about, and work in progress with Angus McAndrew on generalising them to higher-dimensional settings.