Reverse Hypercontractivity and Improved Sampling in High Dimensional Expanders

Explore the concept of reverse hypercontractivity and its applications in high-dimensional expanders in this 58-minute lecture by Yotam Dikstein from the Weizmann Institute of Science. Delve into the connection between reverse hypercontractivity and the mixing of small sets, and discover how many high-dimensional expanders exhibit this property. Examine the relationship between mixing and sampling in high-dimensional expanders, and uncover new Chernoff-like bounds in these fascinating mathematical objects. Learn about the implications of this research, which is based on joint work with Max Hopkins, and gain insights into Boolean function analysis beyond the Boolean cube.