Pablo Soberón 'Mass partitions, transversals, and Stiefel manifolds' | Big Seminar

It is our pleasure to share the Big Seminar talk "Mass partitions, transversals, and Stiefel manifolds" by Pablo Soberón.

Abstract:

We study mass partition problems related to geometric transversals. In this talk, we focus on two problems. In the first, given a measure in R^d, we seek to split R^d into few convex sets of equal measure so that every hyperplane misses the interior of many regions. In the second, we extend recent ham sandwich results on Grassmannians to impose geometric constraints on the dividing subspaces. The topological backbone of both problems is the same, and relies on extensions of the Borsuk—Ulam theorem to Stiefel manifolds. The contents of this talk are joint work with Ilani Axelrod-Freed and Michael Manta.