Workshop on André–Oort problems
Friday, 16 November 2018
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.
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.
Talk 1: 9h30 ‐ 10h30
The André–Oort conjecture: statement and motivation
Coffee break: 10h30 ‐ 11h
Talk 2: 11h ‐ 12h
Introduction to o-minimal structures
Lunch: 12h ‐ 13h45
Talk 3: 13h45 ‐ 14h45
The Manin-Mumford conjecture for algebraic tori
Coffee break: 14h45 ‐ 15h15
Talk 4: 15h15 ‐ 16h15
The proof of the André–Oort conjecture
The workshop will take place in Room 404 of the Mathematical Institute of Universität Freiburg.
The building is located at Ernst-Zermelo-Str. 1, which is within approximately five minutes of the central train station by foot.
If you would like to attend the workshop, please complete our very brief registration form.
Enrico Bombieri and Jonathan Pila.
The number of integral points on arcs and ovals.
Duke Math J., 59(2):337–357, 1989.
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.
Diophantine approximations on definable sets.
Selecta Math. (N.S.), 24(2):1633–1675, 2018.
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.
O-minimality and the André–Oort conjecture for Cn.
Ann. of Math. (2), 173(3):1779–1840, 2011.
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.
Jonathan Pila and Alex Wilkie.
The rational points of a definable set.
Duke Math. J., 133(3):591–616, 2006.
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.