Problems in Conformal Mapping Theory

California Institute Of Technology, Pasadena CA

Investigators

Abstract

ABSTRACT This is a project in the conformal mapping subfield of complex analysis and stochastic processes. Its goal is to solve several well-known problems concerning conformal maps and their applications. The main topics of the study are the following: (i) conformal welding, (ii) universal spectrum of harmonic measure, (iii) diffusion-limited aggregation and other processes with critical behavior. Conformal mapping theory is a classical area of complex analysis; it is an important tool in the study of geometric invariants. The phenomenon of conformal invariance is manifest in many mathematical structures as well as in certain physical theories (conformal field theory and statistical mechanics). The project deals with metric and universality properties of some key conformal invariants, and with conformally invariant probabilities and processes.