Combinatorial positivity by geometric degeneration


               Ezra Miller (University of Minnesota)

Abstract:

The cohomology classes corresponding to orbit closures of group
actions on vector spaces are often ``universal'' in some sense.
As polynomials, these classes also tend to have interesting
combinatorial expansions into sums of simpler pieces, with positive
coefficients.  I will explain how these combinatorial expansions
can be seen to arise geometrically, by exploring a specific case
arising in the representation theory of quivers.  This talk is
about joint work with Mark Shimozono and Allen Knutson, motivated
by a conjecture of Anders Buch and Bill Fulton.