Harold J. Gay Lecture Series
Speaker: Tristan Rivière (Professor, Department of Mathematics Eidgenössische Technische Hochschule Zürich, Switzerland)
Title: ``Looking at 2 Spheres in R^3 with a Morse Theoretic Perspective''
Abstract: ``In their attempt to generalize Euler elastic theory of beams to flexible membranes,
Sophie Germain and Siméon Poisson introduced, two centuries ago, a lagrangian which has now become a
mathematical object whose study goes a way beyond the mechanics of bent surfaces. The so called Willmor
Lagrangian is a functional that shows up in many areas of sciences such as conformal geometry,general relativity, cell biology, optics...etc.
We will try to shed some lights on the universality of this Lagrangian.
One remarkable fact is a quantization phenomenon of the Willmore critical spherical membranes which happen to have all integer valued energy.
We shall then present the project of using the Willmore energy as a Morse function for studying the fascinating space of immersed 2-spheres in the euclidian 3 space and relate topological obstructions in this space to integer values and minimal surfaces.''