Gromov-Witten invariants of GIT quotients -- 
Ionut Ciocan-Fontanine, October 24, 2003

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I will discuss some conjectures about the relationship
between the genus zero Gromov-Witten invariants of a non-abelian
GIT quotient X//G, and those of the associated abelian quotient
X//T, for T a maximal torus in G. These conjectures were inspired
by explicit computations of Gromov-Witten invariants on Grassmannians,
and may be viewed as "quantum" generalizations of results relating
the cohomology rings of X//G and X//T due to Ellingsrud and Stromme,
and Martin. I will then sketch proofs for the conjectures in the
cases when localization methods apply, in particular for all type A
flag manifolds.
This is joint work with Aaron Bertram and Bumsig Kim.