- Cohomological approaches to existence and density of rational points (e.g., obstructions from Brauer groups and descent, torsors)
- Applications of complex geometry to arithmetic (e.g., Zariski density of rational points, deformation techniques and rationally connected varieties, analogies between diophantine approximation and Nevanlinna theory)
- Counting points of bounded height (e.g., asymptotics for Fano varieties, the circle method, arithmetic applications of automorphic forms and harmonic analysis)
- Algebraic geometry over Qbar and height functions (e.g., points of small height)
- Families of abelian varieties (e.g., variation of the Mordell-Weil rank and Tate-Shafarevich group in families)
- Diophantine undecidability (e.g., Hilbert's Tenth Problem over Q, Mazur's conjectures on topology of rational points, and other connections with logic).
Rational points on a K3 surface, created by Ronald van Luijk.
|January 17, 2006 - January 21, 2006||Introductory Workshop in Rational and Integral Points on Higher-Dimensional Varieties|
|March 27, 2006 - March 31, 2006||Cohomological Approaches to Rational Points|
|May 13, 2006 - May 18, 2006||Analytic Methods for Diophantine Equations|