O. Shalom

activity

20202026

most citedMultiple ergodic averages in abelian groups and Khintchine type recurrence

14 citations · 30 across the 16 of their papers we have counts for

collaborators

17 papers

math.DS2026

Non-vanishing of multiple correlation sequences

Or Shalom

We resolve in the negative a conjecture of Frantzikinakis and Kuca concerning the vanishing of multiple correlation sequences in nilsystems. Specifically, we prove the existence of…

math.DS2026

$IP_{rat}$ -polynomial recurrence and large intersections

Borys Holikov, Or Shalom

Let $p_{1}, ..., p_{k}$ be a rationally independent sequence of integer valued nonlinear polynomials. We show that for all $E \subseteq N$ , every Folner sequence $Φ$ , and every $…

cs.AI2026

Holistic Evaluation and Failure Diagnosis of AI Agents

Netta Madvil, Gilad Dym, Alon Mecilati +12

AI agents execute complex multi-step processes, but current evaluation falls short: outcome metrics report success or failure without explaining why, and process-level approaches s…

math.DS2026

On the Furstenberg-Katznelson constant for the IP Szemeredi theorem over finite fields

Or Shalom

Bergelson et al. observed that Furstenberg's proof of Szemeredi's theorem provides a positive lower bound on the density of arithmetic progressions in sets of positive density in t…

math.DS2026

Polynomial towers and inverse Gowers theory for bounded-exponent groups

Asgar Jamneshan, Or Shalom, Terence Tao

In this paper we develop Host--Kra and inverse Gowers theory for abelian groups of bounded exponent. We show that the Host--Kra factors $Z^{\leq k} (X)$ associated with act…

math.DS2025

Ergodic averages and the large intersection property along IP sets

Bryna Kra, Or Shalom

We study multiple ergodic averages along IP sets, meaning we restrict iterates in the averages to all finite sums of some infinite sequence of natural numbers. We give criteria for…

cs.LG2024

Mitigating Data Injection Attacks on Federated Learning

Or Shalom, Amir Leshem, Waheed U. Bajwa

Federated learning is a technique that allows multiple entities to collaboratively train models using their data without compromising data privacy. However, despite its advantages,…

math.DS2023

On the maximal spectral type of nilsystems

Ethan Ackelsberg, Florian K. Richter, Or Shalom

Let $(G /Γ, R_{a})$ be an ergodic $k$ -step nilsystem for $k \geq 2$ . We adapt an argument of Parry to show that $L^{2} (G /Γ)$ decomposes as a sum of a subspace with discrete spectrum and a…

math.DS2023

The structure of totally disconnected Host--Kra--Ziegler factors, and the inverse theorem for the $U^{k}$ Gowers uniformity norms on finite abelian groups of bounded torsion

Asgar Jamneshan, Or Shalom, Terence Tao

Let $Γ$ be a countable abelian group, let $k \geq 1$ , and let $X = (X, X, μ, T)$ be an ergodic $Γ$ -system of order $k$ in the sense of Host--Kra--Ziegler. The $Γ$ -syst…

math.DS2023

A Host--Kra $F_{2}^{ω}$ -system of order $5$ that is not Abramov of order $5$ , and non-measurability of the inverse theorem for the $U^{6} (F_{2}^{n})$ norm

Asgar Jamneshan, Or Shalom, Terence Tao

It was conjectured by Bergelson, Tao, and Ziegler \cite{btz} that every Host--Kra $\F_p^ω$-system of order $k$ is an Abramov system of order $k$ . This conjecture has been verified…

math.DS2023

The structure of non-commutative multiple correlation sequences and applications

Or Shalom

Let $Γ$ be a countable abelian group with Pontryagin dual $Σ := Γ$ . A non-commutative $2$ -fold multiple correlation sequence is a double-indexed sequence $$b(γ,γ') = \int_X T…

math.DS2022★ 8 cited

Khintchine-type recurrence for 3-point configurations

Ethan Ackelsberg, Vitaly Bergelson, Or Shalom

The goal of this paper is to generalize, refine, and improve results on large intersections. We show that if $G$ is a countable abelian group and $φ, ψ : G \to G$ are homomorphisms…

math.DS2021

The structure of arbitrary Conze-Lesigne systems

Asgar Jamneshan, Or Shalom, Terence Tao

Let $Γ$ be a countable abelian group. An (abstract) $Γ$ -system $X$ - that is, an (abstract) probability space equipped with an (abstract) probability-preserving action of…

math.DS2021★ 3 cited

Host-Kra factors for $⨁_{p \in P} Z / p Z$ actions and finite dimensional nilpotent systems

Or Shalom

Let $P$ be a countable multiset of primes and let $G = ⨁_{p \in P} Z / p Z$ . We study the universal characteristic factors associated with the Gowers-H…

math.DS2021★ 14 cited

Multiple ergodic averages in abelian groups and Khintchine type recurrence

Or Shalom

Let $G$ be a countable abelian group. We study ergodic averages associated with configurations of the form ${a g, b g, (a + b) g}$ for some $a, b \in Z$ . Under some assumptions on…

math.DS2021★ 5 cited

Host-Kra theory for $⨁_{p \in P} F_{p}$ - Systems and multiple recurrence

Or Shalom

Let $P$ be an (unbounded) countable multiset of primes (i.e. every prime may appear multiple times) and let $G = ⨁_{p \in P} F_{p}$ . We develop a Hos…

math.DS2020

$⨁_{p \in P} F_{p}$ -Systems as Abramov Systems

Or Shalom

Let $P$ be an (unbounded) countable multiset of primes, let $G = ⨁_{p \in P} F_{p}$ . We study the $k$ 'th universal characteristic factors of an ergodic probabi…

Non-vanishing of multiple correlation sequences

IPrat​-polynomial recurrence and large intersections

Holistic Evaluation and Failure Diagnosis of AI Agents

On the Furstenberg-Katznelson constant for the IP Szemeredi theorem over finite fields

Polynomial towers and inverse Gowers theory for bounded-exponent groups

Ergodic averages and the large intersection property along IP sets

Mitigating Data Injection Attacks on Federated Learning

On the maximal spectral type of nilsystems

The structure of totally disconnected Host--Kra--Ziegler factors, and the inverse theorem for the Uk Gowers uniformity norms on finite abelian groups of bounded torsion

A Host--Kra F2ω​-system of order 5 that is not Abramov of order 5, and non-measurability of the inverse theorem for the U6(F2n​) norm

The structure of non-commutative multiple correlation sequences and applications

Khintchine-type recurrence for 3-point configurations

The structure of arbitrary Conze-Lesigne systems

Host-Kra factors for ⨁p∈P​Z/pZ actions and finite dimensional nilpotent systems

Multiple ergodic averages in abelian groups and Khintchine type recurrence

Host-Kra theory for ⨁p∈P​Fp​- Systems and multiple recurrence

⨁p∈P​Fp​-Systems as Abramov Systems

$IP_{rat}$ -polynomial recurrence and large intersections

The structure of totally disconnected Host--Kra--Ziegler factors, and the inverse theorem for the $U^{k}$ Gowers uniformity norms on finite abelian groups of bounded torsion

A Host--Kra $F_{2}^{ω}$ -system of order $5$ that is not Abramov of order $5$ , and non-measurability of the inverse theorem for the $U^{6} (F_{2}^{n})$ norm

Host-Kra factors for $⨁_{p \in P} Z / p Z$ actions and finite dimensional nilpotent systems

Host-Kra theory for $⨁_{p \in P} F_{p}$ - Systems and multiple recurrence

$⨁_{p \in P} F_{p}$ -Systems as Abramov Systems