Patkós Balázs: Uniform and non-uniform set system problems for disjointness patterns

The most number of sets without two of them being disjoint was determined by Erdős, Ko, and Rado both in the uniform and in the non-uniform case. 
The most number of sets in a set system without s pairwise disjoint sets is not completely determined neither in the uniform case (Erdős matching conjecture) nor in the non-uniform case (Kleitman's problem).
In this talk, I shall give a brief history of these problems, show some new results, and introduce a general setting for considering disjointness patterns. 
Based on joint work with Ryan Martin.