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Russ Woodroofe: The Erdős-Ko-Rado theorem, a theorem of algebraic geometry

Date: 20. 4. 2020
Source: Discrete mathematics seminar
Torek, 21. 4. 2020, od 10h do 12h, na daljavo

Povezava do seminarja:

https://zoom.us/j/96413270492?pwd=NTZZbnpMcWlaN3VDd3RnUDJEaWpqZz09

Meeting ID: 964 1327 0492
Password: SeminarDM

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.