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Some geometric aspects of sum sets

Objective

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.

Field of science

  • /natural sciences/mathematics/pure mathematics/geometry

Call for proposal

FP7-PEOPLE-IEF-2008
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Funding Scheme

MC-IEF - Intra-European Fellowships (IEF)

Coordinator

UNIVERSITAT POLITECNICA DE CATALUNYA
Address
Calle Jordi Girona 31
08034 Barcelona
Spain
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 211 133,09
Administrative Contact
Valentí Guasch Brull (Prof.)