Abstract:

A quadratic form over a field F is universal, if it represents all elements of F;
it is anisotropic, if 0 is not represented nontrivially. The m-invariant of F is
the minimal dimension of a universal anisotropic quadratic form; the u-invariant
is the maximal dimension of such a form. We discuss a recent result of Connor Cassady,
listing all possible values of the m-invariant, and compare it with the similar (still open)
problem on the u-invariant.