Speaker:  Pablo Soberon  (Baruch College,  University of New York

Title:  The Central Transversal Theorem Revisited

Abstract:

The central transversal theorem is a common generalization of two key results in discrete geometry: the ham sandwich theorem and the centerpoint theorem.  The goal, given m measures in R^d, is to find an (m-1) dimensional affine space that is “very deep” within each measure.  In this talk, we discuss how recent extensions of the Borsuk-Ulam theorem for Stiefel manifolds can be used to give an elementary proof of this result.  Moreover, this approach allows us to generalize other mass partition results, such as Yao-Yao partitions.