Event Detail

Event Type: 
Number Theory Seminar
Date/Time: 
Tuesday, May 21, 2019 - 16:00 to 16:45
Location: 
Weniger 201

Speaker Info

Institution: 
University of California, Berkeley, Universite Denis Diderot, Paris
Abstract: 

We consider some families of 3-manifolds obtained from surgery along torus knots and study their unified Witten-Reshetikhin-Turaev (WRT) invariants. Thanks to recent computation of the coefficients in the cyclotomic expansion of the colored Jones polynomial for the (2,2t+1)-torus knots, these unified WRT invariants can be neatly expressed as q-hypergeometric series which converge inside the unit disk. Using the Rosso-Jones formula and some rather non-standard techniques for Bailey pairs, we find Hecke-type formulas for these invariants. In the case of +2 surgery we obtain mock theta functions. This is joint work with Kazuhiro Hikami (Kyushu).