**Prof. Frank Morgan**

**Williams College**

**Lecture 1: Monday, April 8, 2019 at 15:30**

**Title**: *The Double Bubble Problem*

**Abstract**: A single round soap bubble provides the least-perimeter way to enclose a given volume of air, as was proved by Schwarz in 1884. The Double Bubble Problem seeks the least-perimeter way to enclose and separate two given volumes of air. Three friends and I solved the problem in Euclidean space in 2000. In the latest chapter, Emanuel Milman and Joe Neeman recently solved the problem in Gauss space (Euclidean space with Gaussian density). The history includes results in various spaces and dimensions, some by undergraduates. Many open questions remain.

**Lecture 2: Wednesday, April 10, 2019 at 15:30**

**Title**: *The Isoperimetric Problem*

**Abstract**: The isoperimetric problem seeks the least-perimeter way to enclose a given volume. Although the answer is well known to be the round sphere in Euclidean and some other spaces, many fascinating open questions remain. Is a geodesic sphere isoperimetric in CP^2? What is the least-perimeter tile of the hyperbolic plane of prescribed area?

**Lecture 3: Thursday, April 11, 2019 at 15:30**

**Title**: The Isoperimetric Problem in Spaces with Density

**Abstract**: Since their appearance in Perelman’s 2006 proof of the Poincaré Conjecture, there has been a flood of interest in positive weights or densities on spaces and the corresponding isoperimetric problem. The talk will include recent results and open questions.

Light refreshments will be given before the talks in the faculty lounge on the 8th floor.