Graph Theory Seminar - Michelle Delcourt

Title: The typical structure of intersecting families

Abstract: Enumerating families of combinatorial objects with given properties and describing the typical structure of these objects are fundamental problems in extremal combinatorics. During this talk, we will focus in particular on the structure of t-intersecting families of permutations on [n]. If time permits, we will explore the structure of intersecting families in a variety of other settings. Main tools include generalizations of the Bollobas set-pairs inequality and Ellis's stability theorem for intersecting families of permutations. This is joint work with József Balogh, Shagnik Das, Hong Liu, and Maryam Sharifzadeh.