Title: Tree Embedding via the Generalized Loewner Equation
Speaker: Vivian Healey
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:
In its most well-known form, the Loewner equation gives a correspondence between curves in the upper half-plane and continuous real functions (called the “driving function” for the equation). We consider the generalized Loewner equation, where the driving function has been replaced by a time-dependent real measure. In the first part of the talk, we investigate the delicate relationship between the driving measure and the generated hull, specifying a class of discrete random driving measures that generate hulls in the upper half-plane that are embeddings of trees. In the second part of the talk, we consider the scaling limit of these measures with the goal of understanding the scaling limit of the associated hulls in the upper half-plane. We particularly focus on distributions on trees converging to the continuum random tree, and we conclude by describing connections to the complex Burgers equation.Date: Tuesday, March 6, 2018