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Some geometric aspects of sum sets

Type of activity
Competitive project
Acronym
GEOSUMSETS
Funding entity
Commission of European Communities
Funding entity code
PIEF-GA-2009-235136 GEOSUMSETS
Amount
211.112,40 €
Start date
2009-09-01
End date
2012-05-31
Keywords
convex geometry, hyperbolic groups, number theory
URL
http://cordis.europa.eu/projects/235136 Open in new window
Abstract
Following the work of Freiman, Ruzsa, Green, and Fields medal winner Bourgain, Gowers, Tao, the sumset problem is investigated. We consider two topics where the geometry of the ambient group has an important role. Firstly we plan to improve the known inequalities for the sum of subsets in the Euclidean spaces using more tools from convex geometry. For abelian groups, various structure theorem is available about sets whose sum with itself is relatively small. In the non-abelian case, only conjectures are circulating. Secondly we plan to test these conjectures for word hyperbolic groups. Here we plan to combine technics related to Szemeredi's Regularity Lemma with the geometric properties of the Cayley graph.
Scope
Europa
Plan
VII Programa Marc de la Unió Europea 2007-2013
Call year
2009
Funcding program
People Specific Programme
Funding subprogram
People
Funding call
Marie Curie Intra-European Fellowships for Career Development (IEF)
Grant institution
European Commission

Participants