Model Theory and interactions with geometry – MODIG

This is a proposal in model theory and its interactions with number theory and algebraic geometry. Model theory is a part of mathematical logic dealing with abstract structures (models) and has a long history of connections to algebra. The goal of this project is to strengthen these interdisciplinary interactions in France while maintaining also the parallel development of "pure model theory" and "applied model theory". The scientific theme at the background of the proposal is the model theory of fields, a domain which is at the core of the most sophisticated applications to Diophantine geometry and where the interplay between pure and applied model theory is particularly striking. We propose three main directions of research - the model theory of fields with operators (differential fields, difference fields, algebraically closed valued fields) - Hrushovski amalgams and dimension - C-minimality, dependence and measures.