"Geometry, Groups and Model Theory."


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 Nazionalità Coordinatore France [FR]
 Totale costo 1˙284˙000 €
 EC contributo 1˙284˙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-2013-CoG
 Funding Scheme ERC-CG
 Anno di inizio 2014
 Periodo (anno-mese-giorno) 2014-06-01   -   2019-05-31


# participant  country  role  EC contrib. [€] 

 Organization address address: RUE GEORGES CLEMENCEAU 15
city: ORSAY
postcode: 91405

contact info
Titolo: Mr.
Nome: Nicolas
Cognome: Lecompte
Email: send email
Telefono: 33169155589
Fax: +331 6915 5599

FR (ORSAY) hostInstitution 1˙284˙000.00

 Organization address address: RUE GEORGES CLEMENCEAU 15
city: ORSAY
postcode: 91405

contact info
Titolo: Prof.
Nome: "Emmanuel, François, Jean"
Cognome: Breuillard
Email: send email
Telefono: +331 69 15 79 49
Fax: +331 69 15 63 48

FR (ORSAY) hostInstitution 1˙284˙000.00


 Word cloud

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

diophantine    model    conjecture    recent    approximate    geometry    problem    theory    spectral    uniform    groups    mathematics    view    combinatorics    group   

 Obiettivo del progetto (Objective)

'Our proposed research lies at the interface of Geometry, Group Theory, Number Theory and Combinatorics. In recent years, striking results were obtained in those disciplines with the help of a surprise newcomer at the border between mathematics and logic: Model Theory. Bringing its unique point of view and its powerful formalism, Model Theory made a resounding entry into several different fields of mathematics. Here shedding new light on a classical phenomenon, there solving a long-standing open problem via a completely new method.

Recent examples of concrete mathematical problems where Model Theory interacted in a fruitful manner abound: the local version of Hilbert's 5th problem by Goldbring and van den Dries, Szemeredi's theorems in combinatorics and graph theory, the André-Oort conjecture in diophantine geometry (Pila, Wilkie, Zannier), etc. In this vein, and building on Hrushovski's model-theoretic work, Green, Tao and myself recently settled a conjecture of Lindenstrauss pertaining to the structure of approximate groups.

Our plan in this project is to put these methods into further use, to collaborate with model theorists, and to start looking through this prism at a small collection of familiar problems coming from combinatorics, group theory, analysis and spectral geometry of metric spaces, or from arithmetic geometry. Among them: extend our study of approximate groups to the general setting of locally compact groups, obtain uniform estimates on the spectrum of Cayley graphs of large finite groups, prove an analogue for character varieties of the Pink-Zilber conjectures in relation with rigidity theory for discrete subgroups of Lie groups, and clarify the links between uniform spectral gaps and height lower bounds in diophantine geometry with a view towards Lehmer's conjecture.'

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