Analytic and Pseudo-analytic Structures

Boris Zilber

As is well-known Hrushovski constructed a series of strongly minimal structures that have no interpretation in algebraic geometry. We discuss his construction and give arguments towards the understanding that the structures that the construction provides are basically similar to classical ones such as complex numbers with extra analytic transcendental functions.

We are going to discuss how, pursuing systematically this approach we can

(i) develop a model-theoretic point of view on transcendental number theory;

(ii) find a generalisation of analytic theory for abstract algebraically closed fields with applications to algebraic geometry.

Address: Mathematical Institute, University of Oxford, 24-29 St.Giles, Oxford, OX1 3LB, UK

E-mail: zilber@maths.ox.ac.uk