Classical enumerative geometry tells us that in 3-space, two lines meet four given lines in generic position. More generally, the Schubert calculus provides us with ways to count the number of m-planes in (m+p)-space that meet m*p given p-planes nontrivially. In this talk, we will see more generalizations and constructive proofs with homotopy methods. Solutions to these geometric problems are feedback laws to control the behavior of a linear system of first-order differential equations.
UIC Algebraic Geometry seminar, 30 August 2000.