Jonathan Tsai, HKU, Hong Kong

The Loewner driving function of periodic curves

Abstract

The classical work of Charles Loewner allows us to represent a curve in the the upper half-plane starting from the boundary by a real-valued function via the Loewner differential equation. This function is called the Loewner driving function of the curve. This theory has played an important role in the development of Stochastic Loewner evolution (by Lawler, Schramm, Werner and others). However, little is understood about the relationship between the driving function and the curve and it is only possible to explictly calculate the driving function of the curve in a few cases. In this talk, we will consider the Loewner driving function of periodic curves in the upper half-plane and obtain some properties of their driving functions. This is joint work with Carto Wong.