REGULARITY

Regularity and Irregularity in Combinatorics and Number Theory

Coordinatore	MAGYAR TUDOMANYOS AKADEMIA RENYI ALFRED MATEMATIKAI KUTATOINTEZET    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Hungary [HU]
Totale costo	1˙776˙000 €
EC contributo	1˙776˙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-ADG_20120216
Funding Scheme	ERC-AG
Anno di inizio	2013
Periodo (anno-mese-giorno)	2013-03-01   -   2018-02-28

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	MAGYAR TUDOMANYOS AKADEMIA RENYI ALFRED MATEMATIKAI KUTATOINTEZET  Organization address address: REALTANODA STREET 13-15 city: Budapest postcode: 1053 contact info Titolo: Ms. Nome: Tiziana Cognome: Del Viscio Email: send email Telefono: +36 1 4838308 Fax: +36 1 4838333	HU (Budapest)	hostInstitution	1˙776˙000.00
2	MAGYAR TUDOMANYOS AKADEMIA RENYI ALFRED MATEMATIKAI KUTATOINTEZET  Organization address address: REALTANODA STREET 13-15 city: Budapest postcode: 1053 contact info Titolo: Prof. Nome: Endre Cognome: Szemeredi Email: send email Telefono: +36 1 4838308 Fax: +36 1 4838333	HU (Budapest)	hostInstitution	1˙776˙000.00

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 Obiettivo del progetto (Objective)

'Regularity and irregularity plays a central role in mathematics. In the present research proposal we will select problems from combinatorics and number theory (including additive combinatorics), where regularity and irregularity appear. In some cases we have to deal, e.g., with arbitrary finite or infinite subsets of natural numbers, where the only information we have is their cardinality, namely, that they are of positive (lower asymptotic) density within the set of all natural numbers or within the interval [1,N] for a large N. In other cases we consider an arbitrary distribution of n points within the unit square, where all we know is the density of our point set. The goal is often to show that certain configurations appear within the arbitrary set of numbers or points. These configurations definitely appear in a random set of numbers or points, but we have to show this for an arbitrary set of numbers or points with certain general properties. In order to reach our goal one can use two well-known methods. The first one is deterministic, often some kind of greedy algorithm. The second is the probabilistic method of ErdÅ‘s, which shows that almost all arrangements of the given points or numbers (or graphs) fulfill the wanted property. A third method, the so called pseudorandom method, was initiated by the PI (together with M. Ajtai and J. Komlós), uses a combination of these. In other cases we have a deterministic set of numbers with certain quasi-random properties, for example, the primes. Randomness was the key idea in the recent breakthrough of Green and Tao, in proving that primes contain arbitrarily long arithmetic progressions. We will deal with 6 groups of problems: (i) finite or infinite sequences of integers, (ii) difference sets and Fourier analysis, (iii) graph and hypergraph embedding theorems, (iv) Ramsey theory, (v) distribution of points in the plane and in the unit square, (vi) regularities and irregularities in the distribution of primes.'