Seminar by Vijay Ravikumar (TIFR, Mumbai)

Title: The Cohomology Ring of the Complex Grassmannian

2014.08.19 | Jane Jamshidi

Date Wed 27 Aug
Time 16:15 17:15
Location 1531-215 (Aud. D3)

The Grassmannian is a simple example of a moduli space, and its geometry is very well understood.  We give an introduction to the geometry of the complex Grassmannian X by studying its cohomology ring H*(X).
First we describe the Schubert varieties of X and show how the corresponding Schubert classes form an additive basis for H*(X).  By relating the intersections of Schubert varieties to the products of Schubert classes, we determine the multiplicative structure on H*(X) with respect to the Schubert basis.  In particular, we describe Pieri's rule for multiplying arbitrary Schubert classes with certain special Schubert classes, and show how it can be used to solve classical problems in enumerative geometry.