Local Configurations for Frankl's Conjecture

Frankl’s conjecture says that for every finite family of finite sets that is closed under union, there is an element that belongs to at least half the sets in the family. Local configurations are families of sets whose presence ensures that Frankl's conjecture holds for any family which is closed under union and contains them. We recently gave an algorithmic version of the main theorem for the classification of local configurations. In this talk we will discuss how this gives new impetus to this line of research by settling open questions and enabling future directions.