REGULARITY

Regularity and Irregularity in Combinatorics and Number Theory

 Coordinatore MAGYAR TUDOMANYOS AKADEMIA RENYI ALFRED MATEMATIKAI KUTATOINTEZET 

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

Mappa


 Word cloud

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

regularity    deterministic    primes    natural    finite    combinatorics    arbitrary    points    configurations    random    square    certain    theory    appear    irregularity    deal       density    infinite   

 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 Erdős, 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.'

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