  Isotropic Quot schemes parameterize rank $r$ isotropic subsheaves of a vector
bundle equipped with symplectic or symmetric quadratic form. We define a
virtual fundamental class for isotropic Quot schemes over smooth projective
curves. Using torus localization, we prescribe a way to calculate top
intersection numbers of tautological classes, and obtain explicit formulas when
$r=2$. These include and generalize the Vafa-Intriligator formula. In this
setting, we compare the Quot scheme invariants with the invariants obtained via
the stable map compactification.
