A Quantum Knot Perspective on Low-Dimensional Topology (virtual)

The colored Jones polynomial is a generalization of the Jones polynomial from the representation theory of the quantum group Uq(sl2), which revolutionized low-dimensional topology by giving many new knot and 3-manifold invariants.

A key question in the study of these quantum invariants is how the polynomial relates to other knot and 3-manifold invariants such as the hyperbolic volume and the boundary slopes of essential surfaces.

In this talk, I will give an overview of related open problems and discuss my recent research with respect to one of the open questions, the slope conjecture, and related applications to low-dimensional topology.