# Rational and integral points on higher-dimensional varieties

May 12 to May 16, 2014

at the

American Institute of Mathematics, San Jose, California

organized by

Tim Browning and Yuri Tschinkel

## Original Announcement

This workshop will be devoted to the study of rational and integral points on algebraic varieties of dimension at least two.

The goal of this workshop is to bring together researchers in algebraic geometry, cohomological methods, and analytic methods to study connections between these perspectives in Diophantine geometry

The main topics for the workshop are:

• existence of points
• distribution of points
• arithmetic of K3 surfaces

## Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Serre's problem on the density of isotropic fibres in conic bundles
by  Efthymios Sofos,  Proc. Lond. Math. Soc. (3) 113 (2016), no. 2, 261-288  MR3534973
Counting rational points on smooth cubic surfaces
by  Christopher Frei and Efthymios Sofos,  Math. Res. Lett. 23 (2016), no. 1, 127-143  MR3512880
Failures of weak approximation in families
by  M. Bright, T. D. Browning and D. Loughran,  Compos. Math. 152 (2016), no. 7, 1435-1475  MR3530447
Rational points on K3 surfaces and derived equivalence
by  Brendan Hassett and Yuri Tschinkel,  Brauer groups and obstruction problems, 87–113, Progr. Math., 320, Birkhäuser/Springer, Cham, 2017  MR3616008
Counting rational points on the Cayley ruled cubic
by  Régis de la Bret\eche, Tim Browning and Per Salberger,  Eur. J. Math. 2 (2016), no. 1, 55-72  MR3454090
Dualit� et principe local-global pour les tores sur une courbe au-dessus de C((t))
by  Jean-Louis Colliot-Thél\ene and David Harari,  Proc. Lond. Math. Soc. (3) 110 (2015), no. 6, 1475-1516  MR3356812
Principe local global pour les espaces linéaires sur les intersections de deux quadriques
by  Jean-Louis Colliot-Thél\`ene