Quantum invariants of surface diffeomorphisms and 3-dimensional hyperbolic geometry

Geometry Topology Seminar
Monday, April 24, 2023 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Francis Bonahon – University of Southern California – fbonahon@usc.eduhttps://dornsife.usc.edu/francis-bonahon/
Thang Le

Please Note: There will be a pretalk 1-1:40pm in Skiles 006.

This talk is motivated by surprising connections between two very different approaches to 3-dimensional topology, and more precisely by the  Kashaev-Murakami-Murakami Volume Conjecture, which relates the growth of colored Jones polynomials of a knot to the hyperbolic volume of its complement. I will discuss a closely related conjecture for diffeomorphisms of surfaces, based on the representation theory of the Kauffman bracket skein algebra of the surface, a quantum topology object closely related to the Jones polynomial of a knot. I will describe partial results obtained in joint work with Helen Wong and Tian Yang.