Seminars/Colloquia/Invited Talks

Seminars

Ken Stephenson

Conformal Geometry of Surfaces: Theory and Practice

PLACE:	Clark 314
EVENT:	CIS Seminar
DATE:	March 27, 2007
TIME:	1:00 - 2:00 PM

Abstract

Conformal geometry is based on "angles" and is, in many ways, the most natural geometry for the surfaces we encounter in both abstract and practical settings. The theory traces back nearly 200 years to Gauss and Riemann and is arguably one of the richest veins in mathematics.
The practice, on the other hand, is only now catching up. I will discuss discrete conformal geometry based on "circle packing", an approach which faithfully captures the theory, yet is highly flexible and computable. I illustrate its uses in flat mapping the human brain, in conformal welding for shape analysis, and in the combinatorics of point distributions, emphasizing the potential significance of "conformal" information. I will end with some speculation (backed up with data) on the "emergent" nature of conformality.

Brief Biography:

Ken Stephenson is a Professor of Mathemtics at the University of Tennessee. He studied classical complex analysis under Walter Rudin, but was captured by the parallel discrete world after seeing William Thurston talk about circle packing. Since then he has been developing discrete complex function theory and computations, and applying the results to problems in conformal mapping, especially medical imaging. His book, "Introduction to Circle Packing", Cambridge University Press, appeared in 2005.