Student Research Grant Focuses on Manifolds with Density

December 23, 2008

Frank Morgan, Professor of Mathematics at Williams College, has garnered yet another grant from the National Science Foundation. The three-year award will allow Morgan and his students to investigate manifolds with density—a generalization of Riemannian manifolds.

Morgan has received NSF research grants over the last three decades, which have fostered a variety of undergraduate research efforts. The new grant will enable Morgan and several of Williams' young mathematical prodigies to build on research they conducted on manifolds last summer.

Manifolds, or topological spaces that are locally Euclidean, can be understood intuitively as surfaces. The researchers plan to tackle manifolds with density, such as Gauss space, using an isoperimetric approach. Isoperimetric problems involve finding a closed curve of fixed length that encloses the greatest area in the plane. They have applications in probability theory, in Riemannian geometry, and in Grigori Perelman's proof of the Poincaré Conjecture.

Morgan, an expert in soap bubble clusters and other aspects of optimal surfaces, is the author of Geometric Measure Theory: A Beginner's Guide (1988), which has been called the "most accessible introduction to the subject." The book offers a framework for understanding the energy minimization and minimal shapes that govern the physical universe. His "Math Chat" column appeared on MAA Online from 1996 to 2001, and he hosted a live, weekly call-in show in local cable TV. Much of this material appears in The Math Chat Book (2000), published by the MAA.

Morgan was just elected vice president of the American Mathematical Society. His three-year term will begin Feb. 1, 2009.

Source: Williams College, Nov. 10, 2008.