Séminaire Logique mathématique ICJ

Projective geometries arising from Elekes-Szabó problems

by Martin Bays (Universität Münster)

Salle 112 Bât Braconnier

Salle 112 Bât Braconnier

I will explain how complex varieties which have large intersections with grids of unbounded size can be seen, exploiting ideas of Hrushovski, to correspond to projective geometries. I will describe how this leads to a precise characterisation of such varieties. Time permitting, I will discuss consequences for generalised sum-product estimates and connections to diophantine problems. This is joint work with Emmanuel Breuillard.