The Joram seminar is a learning seminar intended to present a hot mathematical topic at a technical level to the wider mathematical community, with an emphasis on younger mathematicians. This year the topic will be "Hypercontractivity and Groups", and the speakers are Noam Lifshitz and Guy Kindler (Hebrew University), Nathan Keller (Bar Ilan University) and Dor Minzer (MIT).
The schedule is as follows:
Wednesday July 9
14:30 Colloquium talk by Noam Lifshitz (HUJI): Product mixing in groups
15:30-16:00 refreshments
16:15-17:15 Dor Minzer (MIT): On CSPs, Inverse Theorems and Friends
Thursday July 10
9:30-10:30 Nathan Keller (Bar Ilan University): Intersection theorems and improved covering results for the symmetric group, via hypercontractivity
10:30-11:00 Coffee break
11:00-12:00 Guy Kindler (HUJI): Hypercontractivity and product mixing in compact Lie groups (talk 1)
12:00-13:30 Lunch break
13:30-14:30 Guy Kindler (HUJI): Hypercontractivity and product mixing in compact Lie groups (talk 2)
14:30-15:30 Noam Lifshitz (HUJI): Hypercontractivity and product mixing in compact Lie groups (talk 3)
15:30-16:10 Coffee break
16:10-17:10 Noam Lifshitz (HUJI): Hypercontractivity and product mixing in compact Lie groups (talk 4)
Hope to see you there!
Abstract for the lecture series by Noam Lifshitz and Guy Kindler:
The study of geometric properties of Cayley graphs associated with non-abelian groups is a rich area of research with wide ranging applications. Here, key questions concern properties such as expansion, mixing, diameter, etc. While remarkable progress was made in this area by applying deep results in character theory, such methods seem to be limited to the case of normal Cayley graphs (those generated by unions of conjugacy classes).
In this mini-course we explore a recent approach which seems to sidestep such limitations. Inspired by techniques originally introduced in the study of the (abelian) Boolean Cube, we use a synergy between hypercontractive inequalities and dimensional lower bounds from representation theory to make progress on various problems. In particular, we will present a significant improvement of a bound of Gowers on the measure of product-free subsets in the unitary group SU(n).
Practical information:
For those arriving by car to the seminar, please fill out the form at the following link: https://forms.gle/N3NadE92u1kFJjXVA.
The Joram seminar is in memory of Joram Lindenstrauss (1936-2012).
For information about the seminar and a list of the previous lectures in this series please see Jormam Seminar.
The seminar is supported by the Research Center of the Einstein Institute of Mathematics.
