Combinatorics Seminar: "The Erdős-Ko-Rado theorem, a theorem of algebraic geometry"

Abstract: The Erdős-Ko-Rado theorem gives an upper-bound on the size of a pairwise intersecting family of small subsets of [n].  If the size of the family is near the upper bound, then the family is a star.

A theorem of Gerstenhaber gives an upper-bound on the dimension of a space of nilpotent matrices.  There are generalizations to other Lie algebras, and if the dimension of the space achieves the upper-bound, then the space is the nilradical of a Borel subalgebra.


I'll talk about how to adapt an approach of Draisma, Kraft, and Kuttler to theorems of Gerstenhaber type for the Erdős-Ko-Rado situation.

Host: Martha Precup