Rationality of Fano threefolds of degree 18 over nonclosed fields.- A categorical invariant for geometrically rational surfaces with a conic bundle structure.- Vanishing cycles under base change and the integral Hodge conjecture.- Explicit rationality of some Fano fourfolds.- Unirationality of certain universal families of cubic fourfolds.- Rational curves and MBM classes on hyperk ähler manifolds: a survey.- Marked and labelled Gushel-Mukai fourfolds.- The Igusa quartic and the Prym map. (I) Some Rationality results.- Rationality of Mukai varieties over non-closed fields.- A refinement of the motivic volume, and specialization of birational types.- On the image of the second ell-adic Bloch map.- Supersingular irreducible symplectic varieties.- On the geometry of Fano threefold hypersurfaces.- Symbols and equivariant birational geometry in small dimensions.