A basic problem from the 19th century asks for the degree of the locus of matrices of bounded rank; the answer is given by Giambelli's determinantal formula. Over the last 25 years, many extensions of this formula have been found, including versions related to classical groups, as well as formulas valid in K-theory or other generalized cohomology theories.

I will describe some of these new formulas, as well as an application: computing the genus of a Brill-Noether variety parametrizing special divisors on a curve. Much of this is joint work with William Fulton, Linda Chen and Nicola Tarasca. Speaker(s): Dave Anderson (Ohio State)