An introduction to o-minimality

Talk by Siegfried Van Hille (KU Leuven),
at the Antwerp Algebra Colloquium on February 19, 2021.

In this talk we discuss various properties of o-minimal structures. The goal is to explain how the simple o-minimality property ensures a “tame” geometry, where tame is the idea envisaged by Grothendieck in his “Esquisse d’un progamme”. I will highlight some important algebraic and geometric concepts that are used to prove that a structure is o-minimal. Finally, if time permits, I will also discuss more recent developments in the study of rational points on transcendental sets.