# 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.