Seminar

The Schramm-Loewner Evolutions (SLEs) are a one parameter family of random curves which occur as the scaling limits of a number of discrete random processes. While SLE provides excellent information on the geometry of these processes, all information about the original parametrization of the discrete processes is lost. This talk will describe recent work which approaches this issue by answering the question "what is the optimal order of Hölder continuity for SLE curves under an arbitrary reparametrization?" With this result in hand, we will discuss an application to integration along SLE paths and a few related open conjectures. No knowledge of SLE will be assumed.