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HARMONIC SIGNED

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

Total Cost €

EC-Contrib. €

Partnership

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Outcomes and
results

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.

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

Project "HARMONIC" data sheet

The following table provides information about the project.

Coordinator	BAR ILAN UNIVERSITY Organization address address: BAR ILAN UNIVERSITY CAMPUS city: RAMAT GAN postcode: 52900 website: www.biu.ac.il 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	http://u.math.biu.ac.il/
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

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	BAR ILAN UNIVERSITY BAR ILAN UNIVERSITY Organization address address: BAR ILAN UNIVERSITY CAMPUS city: RAMAT GAN postcode: 52900 website: www.biu.ac.il contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	IL (RAMAT GAN)	coordinator	1˙260˙625.00

Map

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.

Publications

List of publications.
year	authors and title	journal	last update
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 Fugledeâ€™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-RÃos 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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