The Geometry-Topology Seminar concludes for the term with talks by Julien Roger of Rutgers and Rob Kusner of UMass, Amherst.

Roger will speak on:

Title: Quantum Teichmueller theory and conformal field theory

Abstract: The aim of this talk is to investigate the possible connection between the quantum Teichmueller space and a certain type of conformal field theory. I will first introduce the notion of a modular functor arising from conformal field theory, and its applications to low dimensional topology. Then I will describe the construction of the quantum Teichmueller space, emphasizing the relationship with hyperbolic geometry. Finally, I will describe a possible connection between the two constructions, focusing on the notion of factorization rule. The key ingredients here are the Deligne-Mumford compactification of the moduli space and its Weil-Petersson geometry. I will introduce these notions as well.

Kusner’s talk is

Title: Knots and Links as Ropes, Bands and Branched Coverings

Abstract: What is the geometry of tightly knotted rope? How, for example, is its length related to combinatorial or algebraic knot invariants? Or what shapes are typical of tight knots and links? We’ll discuss recent progress on these “ropelength criticality” issues, and also explore some simpler, potentially more computable, ideal geometric models, including one which realizes knots and links as the “fattest” annuli on a Riemann surface branched covering the sphere.