What is Schubert Calculus ? Frank Sottile The Schubert calculus is concerned with all geometric problems that involve determining the linear subspaces of a vector space that have given positions with respect to other fixed, but general, linear subspaces. While on its face this seems to be a topic in linear algebra, such problems are highly non-linear and combinatorial in nature. Today I will give you an idea of some geometric and combinatorial aspects of Schubert calculus while developing enough techniques to answer some simple, but non-trivial problems from the Schubert calculus. This is a prequel to the talk I give on Thursday at 11 and provides some background for my colloquium on Friday.