Speaker
Nikola Sadovek
(MPI CBG Dresden)
Description
In 1988 Goodman and Pollack asked for a necessary and sufficient condition for a family of convex sets in R^d to admit a k-transversal (a k-dimensional affine subspace that intersects each set in the family) for any 0≤k≤d-1. Helly’s classical theorem corresponds to the case k=0, while Goodman, Pollack, and Wenger obtained a condition for k=d-1. In this talk, we will present a solution to the problem for all 0≤k≤d-1. Our methods are topological and are based on a Borsuk-Ulam-type theorem on Stiefel manifolds. This is joint work with Daniel McGinnis.
Author
Nikola Sadovek
(MPI CBG Dresden)