Title: From conformal field theory to Teichmuller theory and back.
Abstract:
One of the approaches to rigorously encoding the mathematical structures
in 2D conformal field theory is the functorial formulation introduced
by G. Segal. The basic geometric objects are Riemann surfaces with
parametrized boundary components and their corresponding moduli spaces.
These spaces lie in the realm of quasiconformal Teichmuller theory.
Ideas from CFT have led us to results in Teichmuller theory, such as
a new refined infinite-dimensional Teichmuller space on which the
Weil-Peterrson metric converges. On the CFT side we now have natural
analytic spaces for rigorously defining CFT, including the determinant
line bundle.
Assuming only minimal background I will discuss these new results,
the motivation and applications.