A geometric proof of an equivariant Pieri rule for flag manifolds

The Pieri formulas describes the multiplication of 
Schubert classes in the equivariant cohomology of 
any manifold of partial flags.  I will describe how 
to use geometric and combinatorial arguments that 
provide a short proof of an equivariant Pieri rule 
in the classical flag manifold. This is joint work 
with Changzheng Li, Vijay Ravikumar, and Mingzhi Yang.