Alexei Skorobogatov is a Professor of Pure Mathematics at Imperial College London. He is the author of Torsors and Rational Points (Cambridge University Press, 2001) and about 60 research papers on arithmetic and algebraic geometry and error-correcting codes. In 2001 he was awarded the Whitehead Prize by the London Mathematical Society.

• List of contributors; Preface; Part I. Lecture Notes: 1. Three lectures on Cox rings Jürgen Hausen; 2. A very brief introduction to étale homotopy Tomer M. Schlank and Alexei N. Skorobogatov; 3. Torsors and representation theory of reductive groups Vera Serganova; Part II. Contributed Papers: 4. Torsors over luna strata Ivan V. Arzhantsev; 5. Abélianisation des espaces homogènes et applications arithmétiques Cyril Demarche; 6. Gaussian rational points on a singular cubic surface Ulrich Derenthal and Felix Janda; 7. Actions algébriques de groupes arithmétiques Philippe Gille and Laurent Moret-Bailly; 8. Descent theory for open varieties David Harari and Alexei N. Skorobogatov; 9. Factorially graded rings of complexity one Jürgen Hausen and Elaine Herppich; 10. Nef and semiample divisors on rational surfaces Antonio Laface and Damiano Testa; 11. Example of a transcendental 3-torsion Brauer–Manin obstruction on a diagonal quartic surface Thomas Preu; 12. Homotopy obstructions to rational points Yonatan Harpaz and Tomer M. Schlank.