The University of Michigan Combinatorics Seminar
Several years ago Terry Tao and I introduced a Littlewood-Richardson
rule based on counting "puzzles", and gave a rather unsatisfying proof
that it worked. In this talk I'll connect puzzles very directly to
Vakil's geometric Littlewood-Richardson rule, showing in particular
that all the Grassmannian subschemes in his construction are reduced
and Cohen-Macaulay. With some new puzzle pieces, we can extend Vakil's
work to equivariant K-theory of Grassmannians.