The u-invariant of a field is the maximal dimension of a nonsingular anisotropic quadratic form over that field,
whose order in the Witt group of the field is finite. By a classical theorem of Elman and Lam, the u-invariant of a linked field
of characteristic different from 2 can be either 0,1,2,4 or 8. The analogous question in the case of characteristic 2 remained open for a long time..
We will discuss the proof of the equivalent statement in characteristic 2, recently obtained in a joint work by Andrew Dolphin and the speaker.