Differential operators on modular forms

A modular form almost dares you to differentiate it; succumbing to the temptation is not without obstacles, but several methods have been devised to overcome these.

In this mostly expository talk, I will discuss some of these methods, together with at least one arithmetic application, as well as a view towards more general types of modular forms.

Some of this work is joint with BU's very own Angus McAndrew and a few other most excellent people.