Vorlesung Modelltheorie und Anwendungen (SS 2013): O-minimality and Diophantine geometry

Lecturer: Dr. Juan Diego Caycedo.
Time and Room: Mi 8-10, SR 318 Mo 16-18, SR 403.
Prerequisites: Logic or Algebra.
Evaluation: There will be an oral exam at the end of the semester. Assistance to the lectures is mandatory (up to two absences allowed).

The lectures will deal with applications of the theory of o-minimalily to Diophantine geometry. More precisely, recent applications of the Pila-Wilkie theorem on counting rational points in definable sets. The basic plan is to cover the basics of o-minimality up to the cell decomposition theorem, the proof of the Pila-Wilkie theorem and, for applications, at least the proof of the Manin-Mumford conjecture (Laurent's theorem) by Pila and Zannier. Further topics may be discussed if time allows.


For an overview of the bigger picture, see [4].