Hypercontractivity is one of those interesting ideas that has been discovered/studied independently by different communities. We will first look at the general definition of hypercontractivity and two different perspectives of it: one from the information theory community and the other from the computer science community. We'll then look at its generalization, i.e. the Brascamp-Lieb inequality and some of its alternate formulations.
This talk is loosely based on Chandra Nair's tutorial https://www.youtube.com/watch?v=oL1YvAEF450