Title: Generically trivial torsors under algebraic groups

Abstract: I will discuss the recent proof, joint with A. Bouthier and K. Cesnavicius, of the Grothendieck-Serre conjecture for algebraic groups over a field: for a field k, a smooth k-group scheme G and a smooth k-variety X, every generically trivial G-torsor over X trivializes Zariski semilocally on X. This was known when G is reductive or when k is perfect.