Asymptotics of combinatorial and topological objects via modular forms

Abstract: The use of modular forms in describing the asymptotic behaviour of interesting objects goes back to the invention of the Circle Method by Hardy and Ramanujan over 100 years ago. In this talk, I'll describe several results in how we can use modular forms and their relations to study newer objects; in particular the distribution over arithmetic progressions and bias in arithmetic progressions of certain combinatorial and topological objects. Finally, I'll talk briefly about some ongoing work that describes the asymptotic behaviour of a Nahm-type sum which displays much more intricate behaviour than classical modular objects.

Parts of this talk will be based on works with various combinations of Kathrin Bringmann, Giulia Cesana, Will Craig, Amanda Folsom, Ken Ono, Larry Rolen, and Matthias Storzer.

Mathematics

Audience: researchers in the topic

Comments: Meeting ID: 678 4319 0638 Passcode: 999070

UBC (online) Number Theory Seminar