Abstract: I will give an overview of some application of model theory to problems in the extremal combinatorics of incidences. Orchard problems ask for large finite configurations of points on the Euclidean plane (or similar) for which many lines contain three points. The Elekes-Szabó theorem and its variants solve large classes of problems of this character, by exposing the role that algebraic groups must play in such configurations. I will discuss some aspects of the recent development of these ideas, touching in the process on joint works with Emmanuel Breuillard, with Jean-François Martin, and with Jan Dobrowolski and Tingxiang Zou.
univienna.zoom.us/j/63166383248