Just as the number of real roots of a real univariate quadratic
depends on the sign of the discriminant, the topological behavior of real
zero sets depends on (more general) A-discriminant variety complements.
More recently, in numerical linear algebra (and nonlinear work of Shub, Smale,
Beltran, Pardo, and other authors), the relationship between the numerical
behavior of zero sets and distance to the discriminant variety has been
In this talk, we review some of the connections between