WILLIAMSTOWN, Mass., Dec. 5, 2008 – The National Science Foundation has announced the award of a three-year $145,445 grant to Frank Morgan, the Webster Atwell '21 Professor of Mathematics at Williams College.
Morgan and his students will research manifolds with density, a generalization of Riemannian manifolds, long prominent in probability and of rapidly growing interest in geometry. Manifolds, or topological spaces that are locally Euclidean, can be understood intuitively as surfaces. This work will build on research conducted by Morgan and his students over the summer.
Specifically, Morgan intends to approach this area by studying isoperimetric problems manifolds with density such as Gauss space, the premier example of a manifold with density. Isoperimetric problems, which involve finding a closed curve of fixed length, which encloses the greatest area in the plane, have applications in probability theory, in Riemannian geometry, and in Perelman's proof of the Poincaré Conjecture.
Morgan, who has held NSF research grants since 1977, is respected for his undergraduate teaching and promotion of mathematics, through lecturing at a broad spectrum of venues ranging from popular forums and high schools to university colloquia and research seminars.
Recently, Academic Press published the fourth edition of Morgan's book, "Geometric Measure Theory: A Beginner's Guide." Called "the most accessible introduction to the subject," this book offers a clear framework to understand the energy minimization and minimal shapes that govern the physical universe.
Geometric measure theory provides the framework to understand the structure of a crystal, a soap bubble cluster, or a universe. Over the past 50 years it has contributed to major advances in geometry and analysis, including the original proof of the positive mass conjecture in cosmology.
"Geometric Measure Theory" discusses cutting-edge results in this field, emphasizing geometry over technicalities. Its format employs illustrations, exercises, and extensive references. Since its initial publication in 1988, it has been translated into Japanese and Russian.
Morgan is known for work that validated mathematically the conjecture that the double soap bubble is the optimal shape for enclosing two separate chambers of air. He specializes in geometry, minimal surfaces, geometric measure theory, and the calculus of variations.
Morgan's passion for studying bubbles began early, as indicated by a photograph on the inside page of "Geometric Measure Theory," which shows Morgan as a toddler gazing contemplatively at clusters of soap bubbles being blown by his mother. Much of Morgan's academic career has focused on these enigmatic natural forms. Soap bubble clusters and froths model biological cells, liquid crystals, fire-extinguishing foams, bread, cushions and many other materials and structures. "Soap bubbles," Morgan has said, "continue to confound and amaze mathematicians."
Morgan is the Webster Atwell '21 Professor of Mathematics at Williams College. The author of six books and over 150 papers, Morgan won the inaugural National Distinguished Teaching Award in 1992. He joined Williams College in 1987 and has also taught at Princeton University, Stanford University, Rice University, and the Massachusetts Institute of Technology. Morgan formerly had a live, weekly call-in show on local cable TV and a biweekly Match Chat column in national publications. These two platforms grew into "The Math Chat Book," published by the Mathematical Association of America in 2000.
He earned his S.B. from the Massachusetts Institute of Technology in 1974 and his Ph.D. from Princeton University in 1977.
Founded in 1793, Williams College is the second oldest institution of higher learning in Massachusetts. The college's 2,000 students are taught by a faculty noted for the quality of their teaching and research, and the achievement of academic goals includes active participation of students with faculty in their research. Students' educational experience is enriched by the residential campus environment in Williamstown, Mass., which provides a host of opportunities for interaction with one another and with faculty beyond the classroom. Admission decisions are made regardless of a student's financial ability, and the college provides grants and other assistance to meet the demonstrated needs of all who are admitted.
To visit the college on the Internet:www.williams.edu
News: Yue-Yi Hwa