Louisa Liles
The Ohio State University
Title
(t,q)-Series Invariants of Seifert Manifolds
Abstract
This is the third of a three-part lecture series on quantum invariants of 3-manifolds. Previously we discussed the GPPV q-series and Lattice homology. In this talk we will introduce a common refinement of these two invariants, which lives in a larger family of two-variable series developed by Ackhmechet, Johnson, and Krushkal. The speaker and Eleanor McSpirit provided the first known calculations of these new invariants for infinite families of manifolds-- first Brieskorn spheres, then Seifert fibered manifolds. We used these results to establish radial limits and quantum modularity properties whenever the t variable is fixed to be a root of unity. The resulting radial limits give rise to a novel family of $\zeta$-deformed WRT invariants, where $\zeta$ is any root of unity.