One of the most successful applications of model theory to other areas of mathematics is Hrushovski’s work on approximate subgroups about a decade ago. This work led to the celebrated structure theorem on finite approximate subgroups by Breuillard, Green and Tao. Hrushovski’s idea was rooted in geometric stability theory, bringing to bear the rich structure theory of stable groups. This work manifests how model theory, group theory, and combinatorics are deeply intertwined, and has broadened the connections between these three areas, leading to fruitful developments in the past decade. One of the most important results in this direction is Hrushovski’s recent work on the Lie model theorem for all approximate subgroups.

This conference will bring together specialists from pure model theory, whose research focuses on the internal developments of classification theory and geometric model theory, with researchers working on applications of model theory in group theory and (in particular additive) combinatorics. Our aim is to further exchanges and new interactions between these communities, showcasing at the conference major recent developments in these fields, with an emphasize on the mutually fruitful aspects of these research directions.