the u-invariant of a field is defined to be the maximal dimension (number of variables) of a quadratic form which has no nontrivial zeros. although there are some expectations for what u-invariants should be of most "naturally occuring" fields, these invariants are unknown in a great number of situations. for example, if $f$ is a nonreal number field, it is known that $u(f) = 4$, and it is expected that the u-invariant of the rational function field $f(t)$ should be $8$. at this point, however, there is no known bound for $u(f(t))$ (and no proof it is even finite). important progress on this type of problem was obtained by parimala and suresh late last year, who showed that the u-invariant of a rational function field $f(t)$ is $8$ when $f$ is $p$-adic ($p$ odd). in this talk i will describe joint work with david harbater and julia hartmann in which we give an independent proof and a generalization of this result using the method of ``field patching."