### The structure of intersecting families of sets

John Talbot
*Oxford*

The Erdos-Ko-Rado theorem tells us how large an intersecting family of
r-sets from an n-set can be, while a result due to Lovasz gives bounds on
the number of singletons that can occur as intersections of sets from such
a family.
After giving a gentle introduction to this area we consider a more general
problem. Given an intersecting family of r-sets from an n-set how many
k-sets can occur as intersections of sets from the family? For k=r and
k=1 this reduces to the problems described above. We solve some new
cases of this problem and give a conjecture for the general case that is
proved to be assymptotically correct.