Optimal Geometry

Research Interests of John M. Sullivan

My research in optimal geometries involves a combination of mathematical theory and numerical experiments. Many real-world problems can be cast in the form of optimizing some feature of a shape; mathematically, these become variational problems for geometric energies. A classical example is the soap bubble which minimizes its area while enclosing a fixed volume; this leads to the study of the constant mean curvature surfaces found in foams. Cell membranes are more complicated bilayer surfaces, and seem to minimize an elastic bending energy known as the Willmore energy; this bending energy can also be used for mathematical purposes like turning a sphere inside-out. I have also studied energies for knots (which may lead to algorithms for simplifying and recognizing knots), and singularities in bubble clusters and foams.

More details about my research efforts in optimal geometry and related areas of fundamental mathematics are online here; this work has been supported by the National Science Foundation. I have also been involved with more interdisciplinary research efforts, studying foams (with support from NASA), and studying issues in computational geometry for the simulation of casting and extrusion of metals at CPSD. More information about my grant support can be found here online.