#
Rational and integral points on higher dimensional varieties

December 11 to December 20, 2002
at the

American Institute of Mathematics,
San Jose, California

organized by

Bjorn Poonen and Yuri Tschinkel

## Original Announcement

This workshop will be devoted to
the study of rational and integral points on algebraic varieties,
primarily those of dimension at least two.
We are bringing together researchers in algebraic geometry,
diophantine approximation, cohomological methods (e.g. the
Brauer-Manin obstruction, universal torsors), analytic methods
(e.g. the circle method), and algorithmic arithmetic geometry.
We hope especially to facilitate communication between researchers
studying theoretical aspects and those with a more computational bent.

The main questions to be addressed concern

- existence of points,
- distribution of points in various topologies, and
- distribution with respect to heights.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

**Lecture Notes:**

- Colliot-Thelene 1: Rational points on surfaces with a pencil ...
- Colliot-Thelene 2: Rational points on surfaces with a pencil ...
- de Jong: Rationally Connected Varieties
- Graber: Rationally Connected Varieties
- Harari 1: Weak approximation on algebraic varieties (introduction)
- Harari 2: Weak approximation on algebraic varieties (cohomology)
- Hassett 1: Equations of Universal Torsors
- Hassett 2: Weak approximation for function fields
- Heath-Brown: Rational Points and Analytic Number Theory
- Mazur: Families of rationally connected subvarieties
- Peyre: Motivic height zeta functions
- Raskind: Descent on Simply Connected Algebraic Surfaces
- Rotger: Rational points on Shimura varieties
- Salberger: Arithmetic Bezout and Rational Points of Bounded Height
- Skorobogatov: Counterexamples to the Hasse Principle...
- Vojta: Big semistable vector bundles
- Wooley: The Circle Method
- Yafaev: Descent on certain Shimura curves

**Problems**

List of open problems

Photos

Miscellaneous Photos

**Glossary**