Amanda Folsom

Affiliation: Amherst College

Title Of Talk: $q$-series and quantum modularity

Abstract: $q$-series identities within the unit disk and at roots of unity on its boundary play important roles in the intersecting areas of $q$-hypergeometric series, partition theory, and modularity. For example, part of Ramanujan’s original 1920 characterization of his mock theta functions implies that they are $q$-hypergeometric series for which there are theta functions compensating for their exponential asymptotic growth as $q$ radially tends towards suitable roots of unity. Cohen and Zagier have established related identities in other contexts more recently, along with many others. We will offer a brief overview of this topic, and also present new results which establish quantum modularity of related $q$-series and identities. Some of what we present in this talk is preliminary joint work with J. Dousse (Geneva) and J. Lovejoy (Paris).

WARNING: This page contains MATH-JAX

Last update made Tue Mar 10 21:28:03 CDT 2026.
Please report problems to: fgarvan@ufl.edu