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Studies in Harmonic Analysis and Discrete Geometry: Tilings, Spectra and Quasicrystals

Total Cost €


EC-Contrib. €






 HARMONIC project word cloud

Explore the words cloud of the HARMONIC project. It provides you a very rough idea of what is the project "HARMONIC" about.

tile    conjecture    discrete    admit    lies    2000    fundamental    themes    multiple    1974    harmonic    1980    spots    concerning    euclidean    periodic    lot    translates    subject    turn    connection    polytope    analytic    analyze    quasicrystals    combination    interplay    questions    science    interaction    continue    directions    difficult    theme    configurations    space    combinatorial    domains    branches    basic    structure    orthogonal    simplicity    characterization    engineering    vast    translations    geometry    received    fourier    tiling    point    patterns    disciplines    extend    bases    mathematics    deals    apparent    function    rigid    lagarias    mathematical    deep    area    answer    intends    consisting    fuglede    crossroads    famous    possibility    involve    concerned    tilings    theory    lie    atomic    discovery    beautiful    experimental    relation    convex    physical    investigation    natural    diffraction    structures    pi    attack    intermediate   

Project "HARMONIC" data sheet

The following table provides information about the project.


Organization address
postcode: 52900

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Israel [IL]
 Project website
 Total cost 1˙260˙625 €
 EC max contribution 1˙260˙625 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2016
 Duration (year-month-day) from 2016-12-01   to  2021-11-30


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    BAR ILAN UNIVERSITY IL (RAMAT GAN) coordinator 1˙260˙625.00


 Project objective

This proposal is concerned with several themes which lie in the crossroads of Harmonic Analysis and Discrete Geometry. Harmonic Analysis is fundamental in all areas of science and engineering, and has vast applications in most branches of mathematics. Discrete Geometry deals with some of the most natural and beautiful problems in mathematics, which often turn out to be also very deep and difficult in spite of their apparent simplicity. The proposed project deals with some fundamental problems which involve an interplay between these two important disciplines.

One theme of the project deals with tilings of the Euclidean space by translations, and the interaction of this subject with questions in orthogonal harmonic analysis. The PI has recently developed an approach to attack some problems in connection with the famous conjecture due to Fuglede (1974), concerning the characterization of domains which admit orthogonal Fourier bases in terms of their possibility to tile the space by translations, and in relation with the theory of multiple tiling by translates of a convex polytope, or by a function. A main goal of this project is to further develop new methods and extend some promising intermediate results obtained by the PI in these directions.

Another theme of the proposed research lies in the mathematical theory of quasicrystals. This area has received a lot of attention since the experimental discovery in the 1980's of the physical quasicrystals, namely, of non-periodic atomic structures with diffraction patterns consisting of spots. Recently, by a combination of harmonic analytic and discrete combinatorial methods, the PI was able to answer some long-standing questions of Lagarias (2000) concerning the geometry and structure of these rigid point configurations. In the present project, the PI intends to continue the investigation in the mathematical theory of quasicrystals, and to analyze some basic problems which are still open in this field.


year authors and title journal last update
List of publications.
2017 Nir Lev, Alexander Olevskii
Fourier quasicrystals and discreteness of the diffraction spectrum
published pages: 1-26, ISSN: 0001-8708, DOI: 10.1016/j.aim.2017.05.015
Advances in Mathematics 315 2019-06-13
2017 Rachel Greenfeld, Nir Lev
Fuglede’s spectral set conjecture for convexpolytopes
published pages: 1497-1538, ISSN: 2157-5045, DOI: 10.2140/apde.2017.10.1497
Analysis & PDE 10/6 2019-06-13
2018 Nir Lev
Fourier frames for singular measures and pure type phenomena
published pages: 2883-2896, ISSN: 0002-9939, DOI: 10.1090/proc/13849
Proceedings of the American Mathematical Society 146/7 2019-06-13
2018 Andrei K. Lerner
A note on weighted bounds for rough singular integrals
published pages: 77-80, ISSN: 1631-073X, DOI: 10.1016/j.crma.2017.11.016
Comptes Rendus Mathematique 356/1 2019-06-13
2019 Bochen Liu
An L2-identity and pinned distance problem
published pages: 283-294, ISSN: 1016-443X, DOI: 10.1007/s00039-019-00482-8
Geometric and Functional Analysis 29/1 2019-06-07
2019 Andrei K. Lerner, Sheldy Ombrosi, Israel P. Rivera-Ríos
Commutators of singular integrals revisited
published pages: 107-119, ISSN: 0024-6093, DOI: 10.1112/blms.12216
Bulletin of the London Mathematical Society 51/1 2019-06-07

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