Soap Bubbles and Mathematics
Professor Frank Morgan
Williams College
A soap bubble is round because the round sphere provides the least-perimeter way to enclose given volume, as was proved mathematically by Schwarz in 1884. Similarly the familiar double bubble, which forms when two bubbles come together, is the least-perimeter way to enclose and separate the two given volumes, although we didn’t prove this until 2000. If space is given a density, very popular since its appearance in Perelman’s proof of the Poincaré conjecture, the question gets even more interesting. The show will include a little guessing contest with demonstrations and prizes. No prerequisites; all welcome.
Frank Morgan works in minimal surfaces and studies the behavior and structure of minimizers in various dimensions and settings. His proof with colleagues and students of the Double Bubble Conjecture is featured at the NSF Discoveries site. Morgan went to MIT and Princeton, where his thesis advisor, Fred Almgren, introduced him to minimal surfaces. He then taught for ten years at MIT, where he served for three years as Undergraduate Mathematics Chairman, received the Everett Moore Baker Award for excellence in undergraduate teaching, and held the Cecil and Ida Green Career Development Chair. Morgan also served at Williams as Mathematics Department Chair and founding director of an NSF undergraduate research project. He is currently Webster Atwell ’21 Professor of Mathematics, Emeritus, and Editor-in-Chief of Notices of the American Mathematical Society.
