UW AGD Seminar: Alex Rodriguez

Given a Jordan curve in the plane, we can associate a circle homeomorphism (conformal welding) via the conformal welding correspondence. These homeomorphisms arise naturally in Teichmuller theory, Mathematical physics and dynamics. In this talk, we will study this correspondence and we will show that given a flexible curve there is a homeomorphism of the plane, conformal off the curve, that maps the curve to positive area. We will also state a more general result involving Hausdorff dimension and explain connections to some open problems.