Construction de courbes sur les surfaces K3 [d'apr\`es   Bogomolov-Hassett-Tschinkel, Charles, Li-Liedtke, Madapusi Pera, Maulik...]
  We report on recent results concerning the construction of curves on K3 surfaces: the proof of the Tate conjecture for K3 surfaces in odd characteristic (after Maulik, Charles and Madapusi Pera), and the construction of infinitely many rational curves on many K3 surfaces (after Bogomolov-Hassett-Tschinkel and Li-Liedtke). 
Olivier Benoist
math.AG