DIMENSION

High-Dimensional Phenomena and Convexity

 Coordinatore TEL AVIV UNIVERSITY 

Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.

 Nazionalità Coordinatore Israel [IL]
 Totale costo 998˙000 €
 EC contributo 998˙000 €
 Programma FP7-IDEAS-ERC
Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
 Code Call ERC-2012-StG_20111012
 Funding Scheme ERC-SG
 Anno di inizio 2013
 Periodo (anno-mese-giorno) 2013-01-01   -   2017-12-31

 Partecipanti

# participant  country  role  EC contrib. [€] 
1    TEL AVIV UNIVERSITY

 Organization address address: RAMAT AVIV
city: TEL AVIV
postcode: 69978

contact info
Titolo: Ms.
Nome: Lea
Cognome: Pais
Email: send email
Telefono: 97236408774
Fax: 97236409697

IL (TEL AVIV) hostInstitution 998˙000.00
2    TEL AVIV UNIVERSITY

 Organization address address: RAMAT AVIV
city: TEL AVIV
postcode: 69978

contact info
Titolo: Prof.
Nome: Boaz Binyamin
Cognome: Klartag
Email: send email
Telefono: 97236406957
Fax: 97236409357

IL (TEL AVIV) hostInstitution 998˙000.00

Mappa


 Word cloud

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concentration    motifs    dimensional    theorems    formulate    geometric    mathematics    theorem    mathematical    body    convexity    convex   

 Obiettivo del progetto (Objective)

'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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