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 (4th ed. 2009); Calculus Lite 2001, republished as Calculus 2012; 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. He has a personal blog and a new blog at the Huffington Post.
Area: geometry, minimal surfaces, geometric measure theory, calculus of variations.
Positions and Awards
C.L.E. Moore Instructor, 1977-79
Chairman, Undergraduate Mathematics Office, 1979-82
Everett Moore Baker Award for excellence in undergraduate teaching, 1982
Cecil and Ida Green Career Development Chair, 1985-86
Williams College, 1987-
Dennis Meenan ’54 Third Century Professor of Mathematics, 1997-2003
Webster Atwell ’21 Professor of Mathematics, 2003-
National Science Foundation research grants, 1977-2006, 2008-
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
Vice-President, Amer. Math. Soc., 2009-2012
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 includes a little guessing contest with demonstrations, explanations, and prizes. No prerequisites. Friends and families welcome.
Popular talk: Baserunner’s Optimal Path
Abstract: What is the fastest path around the bases in baseball? The answer is something between the baseball diamond and a circle.
Colloquium talk: Optimal Pentagonal Tilings.
Abstract: Although regular hexagons, squares, and equilateral triangles are trivially perimeter-minimizing unit-area planar tilings, there is no tiling by regular pentagons. We discuss recently proven perimeter-minimizing tilings by convex pentagons and efforts to remove the presumably unnecessary convexity hypothesis.
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.