New from the Undergraduate Math Conference

During the 17th annual Rose-Hulman Undergraduate Math Conference, Professor Frank Morgan of Williams College announced on Saturday Morning that he, Michael Hutchings of Stanford College, and Manuel Ritori and Antonio Ros of Granada have proved the Double Bubble Conjecture. The Double Bubble Conjecture is that the familiar double bubble (on the right below) is the optimal shape for enclosing and separating two chambers of air, where optimal means minimizes the surface area needed to enclose two chambers of specified volumes. The proof relies on showing the wild competing bubbles with components wrapped around each other (shown on the left) are unstable.  This is done by a new argument involving rotating different portions of the bubble around a carefully chosen axis at different rates.  [Computer graphics by  John M. Sullivan, University of Illinois, www.math.uiuc.edu/~jms/Images/double/.]

The breakthrough came while Morgan was visiting Ritori and Ros at the University of Granada last spring. Their work is supported by the National Science Foundation and the Spanish scientific research foundation DGICYT.

The proof of two equal bubbles was accomplished earlier by Hass, Hutchings, and Schlafly and required the use of a computer to compute the volumes for competing bubbles.  The new proof for the general case involves only ideas, pencil and paper.

Much of the work involved in the earlier proof can be traced to research done by undergraduates under Morgan in his Geometry Group in the SMALL program.  In fact, a group of undergraduates has extended the above theorem to 4-dimensional bubbles.  (More information on the proof of the Double Bubble Conjecture can be obtained from the Williams College press release  and from the MathChat column written by Professor Morgan and the formal research announcement.)

In addition to the announcement of the proof on Saturday morning, Professor Morgan delighted the conference participants with his "Soap Bubble Geometry Contest" on Friday evening.   The conference started on Friday afternoon with an informative and entertaining talk by Nigel Boston on "Cryptography and the Benefits of Ignorance".  Despite the announcement of the proof of the  Double Bubble Conjecture, the focus of the conference remained on the contributed talks by undergraduate students.  There were fourteen contributed talks, on topics ranging from "Large Primes" and "The Irrationality of Pi" to "Bordered Klein Surfaces with Maximal Automorphism Groups" and "Cwatsets and Graph Isomorphism". For more information on the conference  please visit the Conference HomePage.