# Pure Maths Colloquium: David Ellis

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.

 Where: Physics Theatre C When: Nov 24 2022 @ 16.00 Video: Not recorded
 Speaker: David Ellis University of Bristol Title: Hypercontractivity for some non-product spaces, and some applications

Hypercontractive inequalities for functions on product-spaces have found many applications over the last 50 years, in such fields as analysis, theoretical physics, combinatorics and theoretical computer science. Hypercontractive inequalities are known for such product-spaces as $$n$$-dimensional Gaussian space and the $$n$$-dimensional discrete cube, as well as some closely-related non-product spaces such as the $$n$$-dimensional sphere (for all $$n$$). Recently, useful hypercontractive inequalities have been obtained for a much wider variety of non-product-spaces (sometimes under necessary restrictions on the functions concerned): these include a (conditional) hypercontractive inequality for functions on spaces of linear maps, and (unconditional) hypercontractive inequalities for various compact Lie groups. We survey some of these hypercontractive inequalities, and give some applications in group theory and in extremal combinatorics. We expect there to be further applications, for example in theoretical physics.

Based on joint works with Guy Kindler (HUJI), Noam Lifshitz (HUJI) and Dor Minzer (MIT).