Equivariant Chow ring of the quot scheme 

  The quot scheme parameterizes quotient sheaves of the rank n free
sheaf over P^1 of given rank k and degree d.   This smooth variety is 
a compactification of the space of rational curves of degree d in 
the Grassmannain of rank k quotients of C^n.   The ranks of its
homology groups were determined by Stromme, who used the action of
a natural torus on the quot scheme.   In joint work with Linda Chen
and Tom Braden, we give a presentation for the equivariant Chow ring
of the quot scheme.  While we use the formalism of Goresky, Kottwicz, 
and Macpherson, this formalism does not strictly apply, as the 
1-dimensional torus orbits on the quot scheme are not isolated.

   In this talk, I will describe some of the geometry of the quot
scheme and this torus action, and then explain how to extend the 
formalism of Goresky-Kottwicz-MacPherson to obtain a 
presentation of the equivariant Chow ring of the quot scheme.