  Schubert calculus provides algebraic tools to solve enumerative problems.
There have been several applied problems in systems theory, linear algebra and
physics which were studied by means of Schubert calculus. The method is most
powerful when the base field is algebraically closed. In this article we first
review some of the successes Schubert calculus had in the past. Then we show
how the problem of decoding of subspace codes used in random network coding can
be formulated as a problem in Schubert calculus. Since for this application the
base field has to be assumed to be a finite field new techniques will have to
be developed in the future.
