Paul Beirne

Knots, the colored Jones polynomial and stability

In 2006, Dasbach and Lin observed stability in the coefficients of the Nth colored Jones polynomial for alternating knots. This observation and its consequences have sparked a flurry of activity in both number theory and quantum topology. For example, Garoufalidis, Le and Zagier conjectured identities that have a striking resemblance to those occurring in the classical setting of Rogers and Ramanujan. In this talk, we discuss these developments and higher order stability for an infinite family of pretzel links. This is partly joint work with Robert Osburn.