Rachel Greenfeld

activity

20182025

most citedA counterexample to the periodic tiling conjecture

18 citations · 22 across the 8 of their papers we have counts for

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6 papers · 1 filter

math.CA2025

Translational tilings: structured or wild?

Rachel Greenfeld

The study of the structure of translational tilings has captivated mathematicians, scientists, and the general public for centuries and continues to thrive at the crossroads of ana…

math.CA2025

Some variants of the periodic tiling conjecture

Rachel Greenfeld, Terence Tao

The periodic tiling conjecture (PTC) asserts, for a finitely generated Abelian group $G$ and a finite subset $F$ of $G$ , that if there is a set $A$ that solves the tiling equation…

math.CA2023

Tiling, spectrality and aperiodicity of connected sets

Rachel Greenfeld, Mihail N. Kolountzakis

Let $Ω \subset R^{d}$ be a set of finite measure. The periodic tiling conjecture suggests that if $Ω$ tiles $R^{d}$ by translations then it admits at least one periodi…

math.CA2020

Decoupling for fractal subsets of the parabola

Alan Chang, Jaume de Dios Pont, Rachel Greenfeld +3

We consider decoupling for a fractal subset of the parabola. We reduce studying $l^{2} L^{p}$ decoupling for a fractal subset on the parabola ${(t, t^{2}) : 0 \leq t \leq 1}$ to stu…

math.CA2020

The structure of translational tilings in $Z^{d}$

Rachel Greenfeld, Terence Tao

We obtain structural results on translational tilings of periodic functions in $Z^{d}$ by finite tiles. In particular, we show that any level one tiling of a periodic set in…

math.CA2018

Spectrality of product domains and Fuglede's conjecture for convex polytopes

Rachel Greenfeld, Nir Lev

A set $Ω \subset R^{d}$ is said to be spectral if the space $L^{2} (Ω)$ has an orthogonal basis of exponential functions. It is well-known that in many respects, spectral sets "…