Max Glick
The cohomology of the Grassmannian
The Grassmannian Gr(m,n) is the space of dimension m subspaces of a fixed
dimension m+n complex vector space. These generalizations of projective
spaces (the case m=1) play an important role in various branches of
geometry. The cohomology ring of such spaces bear a striking resemblance
to the ring of symmetric functions introduced in Luis' talk. Specifically,
the cohomology ring admits an additive basis, indexed by partitions, which
play the role of the Schur functions, and which multiply according to
similar rules. I will outline the computation of the cohomology ring and
discuss the connection to symmetric functions.