Department of Mathematical Sciences
Colloquium
Friday, December 5th, 2025
11:00AM-11:50AM
Stratton Hall 202
Speaker: Alena Ernst, WPI
Title: Intersecting families in symmetric and linear groups
Abstract: A family of k-subsets of {1,2,…,n} is called intersecting if every two members have a non-empty intersection. Two classical problems in combinatorics ask: How large can such an intersecting family be, and what do the families of maximal size look like?
In this talk, we introduce natural notions of intersection for permutations and address analogues of these classical questions in the symmetric group. We then turn to intersecting families in the finite general linear groups and describe the corresponding extremal results. Throughout the talk, we highlight some of the techniques used to obtain these theorems, including the representation theory of these groups.