Jinyoung Park, Rutgers University

Abstract

I will give an expository talk on a nice paper by our own Prof. Bhargav Narayanan (joint with David Ellis). https://sites.math.rutgers.edu/~narayanan/pdf/symmetric_3_families.pdf .
A family of sets is said to be symmetric if its automorphism group is transitive, and 3-wise intersecting if any three sets in the family have nonempty intersection. This paper proves if F is a symmetric 3-wise intersecting family of [n] then |F|=o(2^n) (so F is tiny).