Modularity: concrete to abstract and back

Tuesday, 22-Oct-2024 

Abstract

Ever since the spectacular success of Wiles and others in the mid-90’s, there has been a continuous stream of advances attaching various types of modular forms to various types of geometric or algebraic objects.  These modularity results tend to be very technical, but as with much of mathematics, it is possible to isolate certain concrete aspects that can be studied independently of the vast abstract machinery.  I plan to illustrate this with some recent examples.