MTH 248, Fall 2000
Topics in Analysis: Conformal Mappings and Univalent Functions
MWF 9:10--10:00 , 128B Physics
Greg Lawler, 128B Physics
Office Hours: To be announced
An active area of research is the interaction between probability
and conformal mappings with a particular emphasis on understanding
the role of conformal invariance in two-dimensional models from
statistical physics. This course will discuss some of the important
results from complex analysis that are used.
The prerequisite for this course is graduate complex variables, Math
245 at Duke or the equivalent. We will start with a review of the
Riemann mapping theorem and then discuss topics such as: distortion
theorems, Beurling projection theorem, extremal length, Loewner
differential equations. While we will primarily emphasize methods
from complex variables, we will also use probabilistic methods
(Brownian motion) when they are useful.
Text
There is no text for the course but a lot of the material
can be found in the books: Duren, Univalent Functions and Pommerenke,
Boundary Behaviour of Conformal Maps.
Last modified: 16 August 00