Frank Morgan

Office: 413-597-2437
Home: 413-458-8652
FAX: 413-597-4061
Frank.Morgan@williams.edu

http://www.williams.edu/Mathematics/fmorgan

Biographical information on Frank Morgan
Publications
Student research supervision

Frank Morgan works in minimal surfaces and studies the behavior and structure of minimizers in various dimensions and settings. He has six books: Geometric Measure Theory: a Beginner's Guide 2000, Calculus Lite 2001, Riemannian Geometry: a Beginner's Guide 1998,  The Math Chat Book 2000, based on his live,.call-in Math Chat TV show and Math Chat column, Real Analysis 2005, and Real Analysis and Applications 2006.

Degrees

Area: geometry, minimal surfaces, geometric measure theory, calculus of variations.

Positions and Awards

Williams College, 1987-
Chair, 1988-94
Dennis Meenan '54 Third Century Professor of Mathematics, 1997-2003
Webster Atwell '21 Professor of Mathematics, 2003-

National Science Foundation research grants, 1977-
Rice, Visiting Assistant Professor, 1982-83
Stanford, Visiting Associate Professor, 1986-87
NSF Math Advisory Committee, 1987-90
Institute for Advanced Study, 1990-91
First National Distinguished Teaching Award, 1992
University of Massachusetts, Adjunct Professor, 1992-
Council, AMS, 1994-97
Queens College, CUNY, Visiting Professor, fall 1994
Distinguished Alumnus Award, William Allen High School, 1995
Princeton, 250-Anniversary Visiting Professorship for Distinguished Teaching, 1997-98
Second Vice-President, Math. Assn. America, 2000-2002 

Recent talks:

Popular talk: Soap Bubbles and Mathematics

Abstract: Soap bubbles continue to confound and amaze mathematicians. Some recent mathematical breakthroughs are due to students. The presentation will include a little guessing contest with demonstrations, explanations, and prizes. No prerequisites. Friends and families welcome.

Colloquium talk: Isoperimetric Double Bubbles in Rⁿ and Other Spaces.

Abstract: The classical isoperimetric theorem (Schwarz, 1884) says that a single round soap bubble in R³ provides the most efficient, least-area way to enclose a given volume of air. The Double Bubble Theorem (Hutchings, Morgan, Ritore, Ros, Annals of Math 2002) says that the familiar double soap bubble provides the most efficient way to enclose and separate two given volumes in R³. More recently there have been partial extensions from R³ to the sphere S³, hyperbolic space H³, the torus T³, and higher dimensions, including some work by undergraduates. Many open questions remain. No specific prerequisites;  undergraduate majors welcome.

Colloquium/research seminar talk: Manifolds with Density

Abstract: Perelman's proof of the Poincaré Conjecture requires placing a positive, continuous "density" function on the manifold. Manifolds with density appear a number of places in mathematics. The premier example, Gauss space (Euclidean space with Gaussian density), is important to probabilists. We'll discuss results and open questions, starting with isoperimetric problems. The grand goal is to generalize all of Riemannian geometry to manifolds with density.