Schubert calculus is a branch of algebraic geometry introduced in the nineteenth century by Hermann Schubert, in order to solve various counting problems of projective geometry. It turns out that the theory of Schur functions, one of the famous symmetric functions, can be applied to compute the counting problems for Grassmannian. In the first part of the talk, I present the aforementioned theory to answer the following counting problem:
"How many lines L intersect four fixed lines in complex 3-spaces?"
For the second part of the talk, I will briefly introduce the development of a vast extension of the Schubert calculus to affine Grassmannians and affine flag varieties. called "the affine Schubert calculus".