Rational Curves on Grassmannians: systems theory, reality, and transversality

We discuss a particular problem of enumerating rational curves on a Grassmannian from several perspectives, including systems theory, real enumerative geometry, and symbolic computation. We also present a new transversality result, showing this problem is enumerative in all characteristics. While it is well-known how this enumerative problem arose in mathematical physics and also its importance to the development of quantum cohomology, it is less known how it arose independently in mathematical systems theory. We describe this second story. Published in ”Advances in Algebraic Geometry Motivated by Physics”, ed. E. Previato, Contemp. Math., 276, AMS, 2001. pp. 9–42.