Abstract :

I shall first discuss the classical Schubert varieties in the Grassmannian and the Flag Variety. I shall then show examples of several affine varieties related to Schubert varieties including examples from Classical Invariant Theory. I shall also present some recent results relating the cotangent bundles to the Grassmannian and the flag variety and affine Schubert varieties in the infinite dimensional flag variety associated to Kac-Moody Lie algebra.