Nathan Keller

activity

20062026

most citedGeometric influences

17 citations · 54 across the 24 of their papers we have counts for

collaborators

Showing math.COShow all

23 papers · 1 filter

math.CO2026

A Complete Intersection Theorem for Large Permutation Groups

Nathan Keller, Andrey Kupavskii, Noam Lifshitz +1

A family of permutations is called $t$ -intersecting if any two permutations in the family agree on at least $t$ elements. We prove that there exists $n_{0} \in N$ such that…

math.CO2023★ 1 cited

Sharp Hypercontractivity for Global Functions

Nathan Keller, Noam Lifshitz, Omri Marcus

For a function $f$ on the hypercube ${0, 1}^{n}$ with Fourier expansion $f = \sum_{S \subseteq [n]} f^(S) χ_{S}$ , the hypercontractive inequality allows bounding norms of $T_ρf=\sum_Sρ^…

math.CO2023

On $t$ -Intersecting Families of Permutations

Nathan Keller, Noam Lifshitz, Dor Minzer +1

We prove that there exists a constant $c_{0}$ such that for any $t \in N$ and any $n \geq c_{0} t$ , if $A \subset S_{n}$ is a $t$ -intersecting family of permutations then$|A|\leq…

math.CO2020

Proof of Tomaszewski's Conjecture on Randomly Signed Sums

Nathan Keller, Ohad Klein

We prove the following conjecture, due to Tomaszewski (1986): Let $X = \sum_{i = 1}^{n} a_{i} x_{i}$ , where $\sum_{i} a_{i}^{2} = 1$ and each $x_{i}$ is a uniformly random sign. Then $\Pr[|X|\l…

math.CO2019

A structure theorem for almost low-degree functions on the slice

Nathan Keller, Ohad Klein

The Fourier-Walsh expansion of a Boolean function $f : {0, 1}^{n} \to {0, 1}$ is its unique representation as a multilinear polynomial. The Kindler-Safra theorem (2002…

math.CO2017

Biased halfspaces, noise sensitivity, and local Chernoff inequalities

Nathan Keller, Ohad Klein

A halfspace is a function $f : {- 1, 1}^{n} \to {0, 1}$ of the form $f (x) = 1 (a \cdot x > t)$ , where $\sum_{i} a_{i}^{2} = 1$ . We show that if $f$ is a halfspace with $\mathb…

A Complete Intersection Theorem for Large Permutation Groups

Sharp Hypercontractivity for Global Functions

On t-Intersecting Families of Permutations

Proof of Tomaszewski's Conjecture on Randomly Signed Sums

A structure theorem for almost low-degree functions on the slice

Biased halfspaces, noise sensitivity, and local Chernoff inequalities

On $t$ -Intersecting Families of Permutations