Allen Knutson: Overview talk: Schubert geometry of some state sums (part 1)

Speaker
Allen Knutson, Cornell University

Abstract
Given a word Q in the generators of a Weyl group, and a permutation w, the
“AJS/Billey formula” is a 5-vertex-style lattice model state sum that produces
a polynomial independent of Q. Indeed, the polynomial has an interpretation
depending only on v = product(Q) and w, as the equivariant cohomology class
of a Kazhdan-Lusztig variety. The state sum arises geometrically as well,
by degenerating the variety to a union of pieces, and then adding up their
individual cohomology classes.

The corresponding 6-vertex-style state sum is (a slight variant of)
Changjian Su’s formula for the Chern-Schwartz-MacPherson class of a
Kazhdan-Lusztig variety. I’ll explain how to define and compute CSM classes
as ordinary classes of some associated varieties.