Workshop on André–Oort problems

Albert-Ludwigs-Universität Freiburg
Friday, 16 November 2018



Topic: The goal of the workshop is to get a feel for the use of logic and o-minimal theory in particular in the study of algebraic geometry, especially as they pertain to Manin–Mumford and André–Oort problems. While we will not be able to present proofs in detail, we do wish to come to grips with the main ideas through the study of well-chosen examples.

Prerequisites: Talks will presume working-level familiarity with techniques of arithmetic geometry. No knowledge of model theory or o-minimality will be required.


All talks will take place in Room 404 of Ernst-Zermelo-Str. 1.

Practical information


If you would like to attend the workshop, please complete our very brief registration form.



Johan Commelin and Brad Drew
Contact the organizers

Selective references

  1. Enrico Bombieri and Jonathan Pila. The number of integral points on arcs and ovals. Duke Math J., 59(2):337–357, 1989.
  2. Lou van den Dries and Chris Miller. On the real exponential field with restricted analytic functions. Israel J. Math., 85(1-3):19–56, 1994.
  3. Philipp Habegger. Diophantine approximations on definable sets. Selecta Math. (N.S.), 24(2):1633–1675, 2018.
  4. Rutger Noot. Correspondances de Hecke, action de Galois et la conjecture d'André–Oort (d'après Edixhoven et Yafaev). Astérisque, (307):Exp. No. 942, vii, 165–197, 2006. Séminaire Bourbaki. Vol. 2004/2005.
  5. Jonathan Pila. O-minimality and the André–Oort conjecture for Cn. Ann. of Math. (2), 173(3):1779–1840, 2011.
  6. Jonathan Pila. O-minimality and Diophantine geometry. In Proceedings of the International Congress of Mathematicians—Seoul 2014. Vol. 1: pp. 547–572. Kyung Moon Sa, Seoul, 2014.
  7. Jonathan Pila and Alex Wilkie. The rational points of a definable set. Duke Math. J., 133(3):591–616, 2006.
  8. Jonathan Pila and Umberto Zannier. Rational points in periodic analytic sets and the Manin–Mumford conjecture. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 19(2):149–162, 2008.