HARMONIC
Financiado
Studies in Harmonic Analysis and Discrete Geometry Tilings Spectra and Quasicr...
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 bra...
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.
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Duración del proyecto: 72 meses
Fecha Inicio: 2016-11-03
Fecha Fin: 2022-11-30
Fecha Fin: 2022-11-30
Línea de financiación: concedida
El organismo H2020 notifico la concesión del proyecto el día 2022-11-30
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2016-STG:
ERC Starting Grant
Cerrada
hace 9 años
Presupuesto
El presupuesto total del proyecto asciende a
1M€
Líder del proyecto
BAR ILAN UNIVERSITY
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5
548.22K€ |
Participante