Abstract: We survey some of the topics that will be discussed during this semester. Among these topics, we will mention the work of Tian and Kollár-Tian which proves Colliot-Thélène’s conjecture on the local-global principle for zero-cycles on geometrically rational surfaces over global function fields, the proof by Bouthier-Česnavičius-Scavia of the Grothendieck-Serre conjecture for arbitrary smooth k-groups, the recent advances on the Grunwald problem by Harpaz-Wittenberg, Demeio and others, and the recent works by Koymans-Pagano, Morgan and others on ranks of Jacobians in families, with applications to the Hasse principle.
Schedule: January 12 at 2 p.m.