(Department of Mathematics, University of Manitoba)
A Correspondence Between Teichmuller Theory and Conformal Field Theory
|Date||Friday, October 19, 2012|
Riemann surfaces are the objects of the category of complex analysis. Teichmuller space (roughly) is the set of conformally inequivalent Riemann surfaces. Conformal field theories are quantum mechanical or statistical field theories which are invariant under infinitesimal rotations and rescalings. Thus in two dimensions they are closely tied to complex analysis. Attempts to provide a rigorous mathematical model of conformal field theory have spawned a great deal of deep mathematics, and were tied (for example) to the development of vertex operator algebras and representation theory of infinite-dimensional Lie algebras.
In this talk, I will give a non-technical introduction to Teichmuller theory. With the remaining time I will explain a correspondence between the two fields which I discovered with David Radnell, and some of the results that this correspondence generates. Joint work with David Radnell of the American University of Sharjah and Wolfgang Staubach of Uppsala University.