HARMONIC SIGNED
Studies in Harmonic Analysis and Discrete Geometry: Tilings, Spectra and Quasicrystals
Total Cost €
0EC-Contrib. €
0Partnership
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Project "HARMONIC" data sheet
The following table provides information about the project.
| Coordinator |
BAR ILAN UNIVERSITY
Organization address contact info |
| 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.
| # | ||||
|---|---|---|---|---|
| 1 | BAR ILAN UNIVERSITY | 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
| 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 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-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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