Atwell Professor of Mathematics, Emeritus
Blogs: Personal blog | Huffington Post blog
Amazon Author Page Google Citations
Areas of Interest
Frank Morgan works in minimal surfaces and studies the behavior and structure of minimizers in various dimensions and settings.
Books
- Geometric Measure Theory: a Beginner’s Guide (5th ed. 2016)
- Calculus Lite 2001, republished as Calculus 2012; Max-Min video on YouTube.
- 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
- SB, MIT, 1974
- MA, Princeton University, 1976 (NSF Fellow)
- PhD, Princeton University, 1977 (NSF Fellow)
- ScD (honorary), Cedar Crest College, 1995
Area: geometry, minimal surfaces, geometric measure theory, calculus of variations.
Positions and Awards
- MIT, 1977-1987
- 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-
- Department Chair, 1988-94, 2015-16
- Dennis Meenan ’54 Third Century Professor of Mathematics, 1997-2003
- Webster Atwell ’21 Professor of Mathematics, 2003-2016
- Webster Atwell ’21 Professor of Mathematics, Emeritus, 2016-
- National Science Foundation research grants, 1977-2006, 2008-2012
- 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 MAA Haimo 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
- Charter Editor, Involve, 2006—
- Vice-President, Amer. Math. Soc., 2009-2012
- Berkshire Community College, Visiting Professor and Special Assistant to the President, Fall, 2014
- Editor-in-Chief, Notices AMS, 2016-2018.
- Baylor, Visting Professor, fall 2018.
- Yale, Visiting Professor, summer 2019.
Sample talks
Soap Bubbles and Mathematics : Popular talk
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. Video: Museum of 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. Video: Museum of Mathematics.
Baserunner’s Optimal Path : Popular talk
Abstract: What is the fastest path around the bases in baseball? The answer is something between the baseball diamond and a circle.
Abstract: What is the fastest path around the bases in baseball? The answer is something between the baseball diamond and a circle.
Optimal Pentagonal Tilings : Colloquium talk
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. Video: Gathering for Gardner 2021.
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. Video: Gathering for Gardner 2021.
Optimal Bubble Clusters in Rn and Other Spaces : Colloquium talk
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. In 2022 Milman and Neeman posted a proof for triple and quadruple bubbles in Rn and the sphere Sn. There are partial results in hyperbolic space and the torus, including some work by undergraduates. Many open questions remain. No specific prerequisites; undergraduate majors welcome. Videos: Abel Prize celebration in Oslo 2020.
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. In 2022 Milman and Neeman posted a proof for triple and quadruple bubbles in Rn and the sphere Sn. There are partial results in hyperbolic space and the torus, including some work by undergraduates. Many open questions remain. No specific prerequisites; undergraduate majors welcome. Videos: Abel Prize celebration in Oslo 2020.
Manifolds with Density : Colloquium/research seminar talk
Abstract: Since their appearance in Perelman’s proof of the Poincaré Conjecture, densities have played a major role in geometry and the isoperimetric problem. We discuss open questions and recent results, some by undergraduates. Video.
Abstract: Since their appearance in Perelman’s proof of the Poincaré Conjecture, densities have played a major role in geometry and the isoperimetric problem. We discuss open questions and recent results, some by undergraduates. Video.
Multiple Bubbles and Densities: Colloquium talk
The round sphere provides the least-perimeter way to enclose prescribed volume in Rm. The n-bubble problem seeks the least-perimeter way to enclose and separate n prescribed volumes in Rm. The solution is known only for n ≤ 5, n ≤ m in Rm (the standard multiple bubble). If you give Rm Gaussian density, the solution was recently proved by Milman and Neeman for all n ≤ m. There is further news for other densities. We’ll describe many such results and open questions. Students welcome. Video.
The round sphere provides the least-perimeter way to enclose prescribed volume in Rm. The n-bubble problem seeks the least-perimeter way to enclose and separate n prescribed volumes in Rm. The solution is known only for n ≤ 5, n ≤ m in Rm (the standard multiple bubble). If you give Rm Gaussian density, the solution was recently proved by Milman and Neeman for all n ≤ m. There is further news for other densities. We’ll describe many such results and open questions. Students welcome. Video.
Optimal Tilings: Colloquium talk
In 2000 Hales proved that regular hexagons provide a least-perimeter way to partition the plane into unit areas. Undergraduates recently obtained a partial extension to closed hyperbolic manifolds. The 3D Euclidean case remains open. The best tetrahedral tile was proved recently. (Despite what Aristotle said, the regular tetrahedron does not tile.) Many open questions remain.
Megamenu Social