# University of Toronto's Symplectic Geometry Seminar

Sept. 20 2004, 1:10 - 2

SS5017A

## Kevin Purbhoo

###
U of Toronto

##
"Coadjoint orbits and vanishing problems in Schubert calculus"

** Abstract: **
Let i:K' -> K be an inclusion of compact groups. There is an induced map
i^*:k^* -> k'^* on the duals of the Lie algebras, and we would like to
calculate the image of a coadjoint orbit under this map. Berenstein
and Sjamaar (2000) gave a solution to this problem in terms of the
cohomology of homogenous spaces K/T and K'/T'. This motivates us to
study Schubert calculus of these spaces, and in particular to understand
vanishing properties of the map H^*(K/T) -> H^*(K'/T') in the Schubert
basis. I will expound this picture, and discuss some techniques
which are applicable to the problem.