Zhijia Zhang, September 18, 2026

Title: Universal torsors and stably rational cubic hypersurfaces

Abstract: In 1985, Beauville, Colliot-Thélène, Sansuc and Swinnerton-Dyer constructed examples of stably rational but irrational varieties, answering a question of Zariski. In this talk, we extend their construction to produce stably rational smooth cubic hypersurfaces over Q, in every dimension greater than one. The key input is the proof of a conjecture of Colliot-Thélène and Sansuc: over a field of characteristic zero, every universal torsor over a quartic del Pezzo surface is rational if it has rational points. Joint with Yuri Tschinkel.