27th Kieval Lecture

Monday, December 2, 1996 @ 8:00 p.m.

Founder's Hall 118.

Minimal surfaces are mathematicians' idealization of soap films. They are of interest to artists and architects, to designers of strong, lightweight structures, and to materials scientists who want to understand the microstructure of compound materials. The lecture will touch on these applications and will also try to explain how computers have become extremely useful in the hunt for minimal surfaces and in their application to physical problems. Computer graphics animations of interest to both scientists and artists will be shown.

Tuesday, Dec. 3, 1996 @ 4:00 pm

Gist Hall 221.

A new turn for Archimedes.

Abstract: A recent issue of the Philosophical Transactions of the Royal
Society of London was devoted to ``Curved surfaces and chemical
structures.'' Differential geometry is playing an important role in the
experimental physics of materials, but in ways that are surprising---and
sometimes troubling for mathematicians. I will discuss this by considering
the paper of Viet Elser in this issue, which purports to construct its
title surface: A cubic Archimedian screw.

We know Archimedes' screw by the name of the helicoid, an embedded minimal
surface. The ways in which a properly embedded minimal surface of
finite topology can diverge is a fundamental question, whose relevance
is underscored by some strong theorems and by some
recently-discovered examples. The helicoid stands as the prototype. There is
hope that the cases yet to be classified consist entirely of surfaces
asymptotic to the helicoid. In the second, less applied, part of the
lecture, I will present some of the evidence as to
why this may be the case.