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DIMENSION

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High Dimensional Phenomena and Convexity

High-dimensional problems with a geometric flavor appear in quite a few branches of mathematics, mathematical physics and theoretical computer science. A priori, one would think that the diversity and the rapid increase of the nu... ver más

31/12/2018

WEIZMANN

998K€

Presupuesto del proyecto: 998K€

Líder del proyecto

WEIZMANN INSTITUTE OF SCIENCE No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

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Financiación concedida El organismo FP7 notifico la concesión del proyecto el día 2018-12-31 No tenemos la información de la convocatoria

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2 Participantes

WEIZMANN

0.00€ | Lider

TAU

N.D. | Participante

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Líder del proyecto

WEIZMANN INSTITUTE OF SCIENCE No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 998K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto High-dimensional problems with a geometric flavor appear in quite a few branches of mathematics, mathematical physics and theoretical computer science. A priori, one would think that the diversity and the rapid increase of the number of configurations would make it impossible to formulate general, interesting theorems that apply to large classes of high-dimensional geometric objects. The underlying theme of the proposed project is that the contrary is often true. Mathematical developments of the last decades indicate that high dimensionality, when viewed correctly, may create remarkable order and simplicity, rather than complication. For example, Dvoretzky's theorem demonstrates that any high-dimensional convex body has nearly-Euclidean sections of a high dimension. Another example is the central limit theorem for convex bodies due to the PI, according to which any high-dimensional convex body has approximately Gaussian marginals. There are a number of strong motifs in high-dimensional geometry, such as the concentration of measure, which seem to compensate for the vast amount of different possibilities. Convexity is one of the ways in which to harness these motifs and thereby formulate clean, non-trivial theorems. The scientific goals of the project are to develop new methods for the study of convexity in high dimensions beyond the concentration of measure, to explore emerging connections with other fields of mathematics, and to solve the outstanding problems related to the distribution of volume in high-dimensional convex sets.

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