Boris Zilber (University of Oxford)
zilber@maths.ox.ac.uk
We consider geometry as a very broad notion and argue that a purely logical criterion for a 'good' mathematical theory explains the central role played by classical geometric theories, such as the theory of compact complex manifolds and algebraic geometry. This broad view on geometric structures led to a classification result and applications in Diophantine geometry and transcendental number theory.
Most recent discoveries show that the adequate context for representing good (Zariski) geometries is non-commutative geometry.