Résume | This will be the first talk on our solution, with John Baldwin and James Freitag, to the Koponen conjecture. As part of Shelah’s program of classifying unstable first-order theories, Koponen proposes to classify simple homogeneous structures, such as the random graph. More precisely, she conjectures (2016) that all simple theories with quantifier elimination in a finite relational language are supersimple of finite rank, and asks (2014) whether they are one-based. In this talk, we give an overview of our solution to the Koponen conjecture, where we show that the answer to this question is yes. |