# MIT COMBINATORICS SEMINAR

# Algebras of Chern forms on flag manifolds and forests

## Alexander Postnikov (MIT)

## Room 2-338

## 4:15 p.m., **Wednesday**, February 11, 1998

Abstract:
The algebra generated by the Chern forms of standard line bundles over the
flag manifold Fl_n is a natural extension of the cohomology ring of Fl_n.
We show that the dimension of this algebra is equal to the number of forests
on n labelled vertices. We present an explicit construction for a monomial
basis. More generally, the results naturally extend to a wider class of
algebras, whose bases are labelled by generalized parking functions.
This is a joint work with Boris Shapiro and Mikhail Shapiro.