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New FWF-project granted

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In its most recent board meeting, the Austrian Science Fund FWF has granted a research project on "The Elekes-Szabo Problem". The project was proposed by Oliver Roche-Newton and Audie Warren, who will also serve as principal investigators.

The Elekes-Szabó Theorem gives an upper bound for the size of the intersection between an algebraic surface and a Cartesian product, subject to certain non-degeneracy conditions on the surface. This rather general theorem has led to many beautiful applications, particularly in discrete geometry. The goals of this project include establishing a version of the Elekes-Szabó Theorem in the finite field setting, and exploring further applications of this result, particularly in the context of sum-product phenomena.