Stiefel Manifolds and Mass Partition Results

Pablo SoberĂ³n, Baruch College/CUNY

Date and time: 2pm (New York time), Tuesday, October 5, 2021

Place: On Zoom (details provided on the seminar mailing list)

Mass partition results, such as the ham sandwich theorem, study how we can split measures or finite sets of points in $\mathbb{R}^d$ given some geometric constraints on the partition. The proofs are often topological, as they rely on parametrizing the space of all possible partitions with a well suited topological space. In this talk we discuss new mass partition results where the parametrization of the space of partitions involves Stiefel manifolds. This includes generalizations of the central transversal theorem, partitions of measures by concentric spheres in $\mathbb{R}^d$, and partitions of families of $k$-dimensional affine subspaces in $\mathbb{R}^d$ using a $d-k-1$ affine subspace as the dividing object.