WORDS

Words and Waring type problems

Coordinatore	THE HEBREW UNIVERSITY OF JERUSALEM.    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Israel [IL]
Totale costo	1˙197˙800 €
EC contributo	1˙197˙800 €
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-2009-AdG
Funding Scheme	ERC-AG
Anno di inizio	2010
Periodo (anno-mese-giorno)	2010-01-01   -   2014-12-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	THE HEBREW UNIVERSITY OF JERUSALEM.  Organization address address: GIVAT RAM CAMPUS city: JERUSALEM postcode: 91904 contact info Titolo: Mr. Nome: Hani Cognome: Ben-Yehuda Email: send email Telefono: +972 2 6586676 Fax: +972 2 6513205	IL (JERUSALEM)	hostInstitution	1˙197˙800.00
2	THE HEBREW UNIVERSITY OF JERUSALEM.  Organization address address: GIVAT RAM CAMPUS city: JERUSALEM postcode: 91904 contact info Titolo: Prof. Nome: Aner Cognome: Shalev Email: send email Telefono: -6583150 Fax: -5629732	IL (JERUSALEM)	hostInstitution	1˙197˙800.00

Mappa

 Word cloud

Esplora la "nuvola delle parole (Word Cloud) per avere un'idea di massima del progetto.

 Obiettivo del progetto (Objective)

Hilbert's solution to Waring problem in Number Theory shows that every positive integer is a sum of g(n) nth powers. Surprising non-commutative analogues of this phenomenon were discovered recently in Group Theory, where powers are replaced by general words. Moreover, the study of group words occurs naturally in important contexts, such as the Burnside problems, Serre's problem on profinite groups, and finite simple group theory. We propose a systematic study of word maps on groups, their images and kernels, as well as related Waring type problems. These include a celebrated conjecture of Thompson, problems regarding covering numbers and mixing times of random walks, as well as probabilistic identities in finite and profinite groups. This is a highly challenging project in which we intend to utilize a wide spectrum of tools, including Representation Theory, Algebraic Geometry, Number Theory, computational group theory, as well as probabilistic methods and Lie methods. Moreover, we aim to establish new results on representations and character bounds, which would be very useful in various additional contexts. Apart from their intrinsic interest, the problems and conjectures we propose have exciting applications to other fields, and the project is likely to shed new light not just in group theory but also in combinatorics, probability and geometry.