## Number Theory Seminar

### Wednesday, June 19th, 2019

**Time:** 3:30-4:30 p.m. **Place:** Jeffery Hall 319

**Speaker:** Robert Osburn (University College Dublin)

**Title:** Generalized Kontsevich-Zagier series via knots

**Abstract:** Over the past two decades, there has been substantial interest in the overlap between quantum knot invariants, q-series and modular forms. In this talk, we discuss one such instance, namely an explicit q-hypergeometric expression for the Nth colored Jones polynomial for double twist knots. As an application, we generalize a duality at roots of unity between the Kontsevich-Zagier series and the generating function for strongly unimodal sequences. This is joint work with Jeremy Lovejoy (Paris 7 and Berkeley).