Dragomir Saric spoke in the Queens College Mathematics Colloquium on October 21, 2009.

Title: Circle Homeomorphisms and Shears

Abstract: The space of homeomorphisms Homeo(S^1) of the unit circle S^1 is a classical topological group which acts on S^1. Homeo(S^1) contains many important subgroups such as: the group Diffeo(S^1) of diffeomorphisms of S^1, the group QS(S^1) of quasisymmetric maps of S^1, the group Symm(S^1) of symmetric maps of S^1, the group Mob(S^1) of Mobius maps which preserve S^1, and many more. The unit circle S^1 is the ideal boundary of the hyperbolic plane H. We explain how to use the hyperbolic geometry of the hyperbolic plane H in order to parametrize the coadjoint orbit spaces Mob(S^1)\Homeo(S^1), Mob(S^1)\QS(S^1) and Mob(S^1)\Symm(S^1). If time permits, we will explain the connections of these coadjoint orbit spaces with the Teichmuller theory.