William Fulton: Degeneracy loci and double Schubert polynomials for the classical groups

In 1849 Cayley gave a few formulas to describe loci defined by matrices of prescribed ranks. Working out general formulas for such loci, in the context of maps of vector bundles, has played an important role in the development of intersection theory in algebraic geometry. This Type A story was largely completed by the 1990's, using the double Schubert polynomials of Lascoux and Schützenberger. The search for analogous formulas for the other classical types B, C, and D has been surprisingly challenging. We will describe the recent success by Ikeda, Mihalcea, and Naruse, with contributions by Anderson and the speaker.