From the Generalized Volume Conjecture to Turaev and Ramanujan

Abstract: In this talk, intended for a broad audience, we will survey the development of a new 3-manifold invariant that provides an answer to questions like this: What do Dedekind eta and Alexander polynomial have in common? In fact, illustrated by this question is perhaps the most attractive feature of this new invariant: it provides new and often unexpected connections between different areas of mathematics. Originating from complex Chern-Simons theory and quantization of $\operatorname{SL}(2,\mathbb{C})$ character varieties, it evaluates to $q$-series expressions that are more commonly seen in the theory of mock modular forms and in logarithmic Vertex Operator Algebras (VOAs). The goal of the talk will be to survey these relations using least amount of technical details.

algebraic geometrynumber theory

Audience: researchers in the topic

Algebraic Geometry and Number Theory seminar - ISTA