CORDIS Project
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This project investigates the sumset problem in mathematics, focusing on the role of geometry in abelian and non-abelian groups. It aims to improve existing inequalities and test conjectures using advanced techniques from convex geometry and group theory.
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 conject…
UNIVERSITAT POLITECNICA DE CATALUNYA
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