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Abstract: In 1884 Schwarz proved that a single round soap bubble provides the least-area way to enclose a given volume of air. In 2002 Hutchings, Morgan, Ritor\'e, and Ros proved that the familiar double soap bubble provides the least-area way to enclose and separate two given volumes. We'll discuss results and open questions in other spaces from $R^n$ to spheres $S^n$, hyperbolic space $H^n$, Gauss space, and tori, including work by undergraduates. No prerequisites; undergraduates welcome.
This talk will be accessible to undergraduates.
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