Abstract:
I will discuss two things in this talk.  First, I will consider
the classical theorem which shows when two subdomains in the upper
half plane are conformally equivalent and describe Loewner evolution
in these domains in terms of a process I call "excursion reflected
Brownian motion".  Second, I will discuss the continuous limit of
the Laplacian random walk --- this is closely related to work of
Zhan on the harmonic random Loewner chain.