Quantum knot invariants and the volume conjecture

Daniel Vitek , Princeton University
Fine Hall 314

I'll sketch some of the basics of quantum topology, including how to get knot invariants from a ribbon category and how to construct non-cocommutative Hopf algebras.  Next we'll turn to hyperbolic geometry and discuss how hyperbolic structures on knot complements arise.  Finally, I'll discuss how these two topics are linked via the volume conjecture, and give some directions of current work.