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

Decoding of Subspace Codes, a Problem of Schubert Calculus over Finite Fields