(Department of Mathematics, University of Manitoba)
The universal Teichmueller space, quasiconformal maps and univalent functions
|Date||Friday, February 29, 2008|
Quasiconformal maps arise naturally in the study of Riemann surfaces. The theory of quasiconformal maps was developed by Ahlfors, Bers and others, drawing on ideas of Teichmueller, in order to study moduli spaces of Riemann surfaces. Quasiconformal maps are now an indispensible part of dynamics, hyperbolic geometry and Teichmueller theory. The universal Teichmueller space is an infinite-dimensional group which in some sense parametrizes the space of all Riemann surfaces.
In this talk I will give an introduction to quasiconformal maps and the universal Teichmueller space. I will emphasize its relation to the set of univalent functions on the disc. All definitions will be provided and no background assumed. Technical details and proofs will be minimized as much as possible.