Russ Woodroofe: The Erdős-Ko-Rado theorem, a theorem of algebraic geometry
Source: Discrete mathematics seminar
Povezava do seminarja:
Meeting ID: 964 1327 0492
Povzetek. 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 a linear algebraic groups approach of Draisma, Kraft, and Kuttler to theorems of Gerstenhaber type for the Erdős-Ko-Rado situation.