Rothschild Prize Symposium: Celebrating Tamar Ziegler’s Work

Date:

Thu, 19/09/202412:00

On September 19 there will be a symposium in mathematics celebrating Tamar Ziegler's work and Rotschild prize with talks by Emmanuel Breuillard, Sarah Peluse, Noam Lifshitz and Amichai Lampert.

For registration and details of the workshop please consult the following link.

Lunch will be provided for those who will register only.

Details on the symposium:

Location: The (new) Israeli National Library, Jerusalem.

Date: September 19, 2025.

Schedule:

12:00-12:50 Prof. Emmanuel Breuillard FRS (Oxford)

Title: Limit theorems and equidistribution on nilpotent Lie groups

Abstract: Generalizing the classical limit theorems of probability theory to non-commutative Lie groups is a long standing question that has been studied since the 1950s. Nilpotent Lie groups form a rich class of groups where such theorems can be formulated. I will discuss joint work with Timothee Benard in which we use a Fourier analytic approach based on a non-commutative Weyl differencing technique on free Lie algebras to establish very complete results regarding the Central Limit Theorem, Berry-Essen bounds and their local counterparts for iid random walks on nilpotent Lie groups. Interesting new phenomena arise in the non-centered setting with applications to equidistribution on homogeneous spaces.

12:50- 14:00 Lunch at the national library (registration required)

14:00- 14:50 Dr. Noam Lifshitz (HUJI)

Title: Product mixing in groups

Abstract: Let A,B,C be subsets of the special unitary group SU(n) of Haar measure \ge e^{-n^{1/3}}. Then ABC=SU(n). In fact, the product abc of random elements a\sim A, b\sim B, c\sim C is equidistributed in SU(n). This makes progress on a question that was posed independently by Gowers studying nonabelian variants of questions from additive combinatorics and settles a conjecture of physicists studying quantum communication complexity. To prove our results we introduce a tool known as ‘hypercontractivity’ to the study of high rank compact Lie groups. We then show that it synergies with their representation theory to obtain our result. Time permitting, I will also discuss corresponding results for finite simple groups, where the relevant representation theoretic notion of `tensor rank’ was introduced only recently independently by Gurevich—Howe and Guralnick—Larsen—Tiep.
Based on my joint works with Ellis—Kindler—Minzer; Filmus—Kindler—Minzer; Keevash; Evra—Kindler; and Evra—Kindler—Lindzey.

15:00-15:50 Dr. Amichai Lampert (Michigan)

Title: Density of rational solutions to polynomial equations in many variables

Abstract: Let $K$ be a field. Call it a Birch field if for any odd $d$ , any equation of the form $a_1x_1^d+\ldots+a_nx_n^d = 0$ with $a_i\in K$ admits a non-trivial rational solution, provided $n$ is sufficiently large. Number fields are Birch fields, among many other examples. In 1957, Birch proved that if $K$ is a Birch field, then any system of homogeneous equations of odd degrees over $K$ admits a non-trivial rational solution, provided the number of variables is sufficiently large. We will present a recent improvement of Birch's result, which gives a uniform upper bound on the codimension of the Zariski closure of the set of rational points (for fields of characteristic zero). The bound depends only on $K$ and the degrees of the equations involved. Joint work with Andrew Snowden.

16:30-17:20 Prof. Sarah Peluse (Stanford)

**Talk broadcasted in the lecture hall.**

Title: Sqorners

Abstract: I'll talk about recent work with Sean Prendiville and Fernando Shao in which we prove the first quantitative bounds in Bergelson—Leibman’s multidimensional polynomial Szemer\’edi theorem for the configuration (x,y), (x,y+d), (x+d^2,y), which we call “sqorners”. We also prove a “popular difference” version of this result, with effective bounds