Hypercontractivity is a fundamental concept in Boolean function analysis. Reverse hypercontractivity is its lesser-known sibling, which is connected with the mixing of small sets. We will introduce reverse hypercontractivity and show that many high-dimensional expanders have this property. Along the way, we will see the connection between mixing and sampling in high-dimensional expanders and discover new Chernoff-like bounds in these marvelous objects.

This talk is based on joint work with Max Hopkins.

Video Recording