Geometry and Topology Seminar

Solutions to classical geometric variational problems are often unique and nice: the ball is the only shape which minimizes surface area among shapes of equal volume. But the solutions to the variational problems of the Alexandrov-Fenchel inequalities are conjectured (by R. Schneider) to be non-unique and wild. I will talk about these variational problems, including their connections to areas beyond convexity such as analysis and combinatorics, and how we resolved some of these conjectures. Joint work with Ramon van Handel.