Some Hilton-Milner type theorems

The Erdős-Ko-Rado theorem describes the largest family of pairwise-intersecting k-element subsets of a fixed base set: for small k, this is the family of all sets containing some common element.  The Hilton-Milner theorem describes what happens if we disallow a common element.

I will present recent progress from joint work with Denys Bulavka and Francesca Gandini on the Hilton-Milner theorem and extensions.