For the most part, we will be following Lou van den Dries’ book Tame Topology and O-minimal Structures for this seminar. We will supplement with material from reseach papers. If there are specific theorems about o-minimality you would like to see this term, let me know. Some possible topics include
- Speissegger’s theorem on Pfaffian closures of o-minimal structures
- The Peterzil-Starchenko o-minimal trichotomy
- The Pila-Wilkie counting theorem
- Proofs of o-minimality of specific structures (e.g. $\mathbb{R}_{an,\exp}$ or the expansion by Gevrey functions)
- The Peterzil-Starchenko o-minimal Chow theorem