Title: Schubert calculus by counting puzzles
| Speaker | Allen Knutson |
| Affiliation | Cornell |
| Location | MC 5479 |
Abstract: There are three rings-with-bases whose multiplicative structure constants are computed by the same rule: the cohomology ring of the Grassmannian Gr(k,n), the representation ring of GL_k (made by stabilizing the previous in n), and one made by summing all representation rings of the symmetric groups (made by stabiliizing the previous in k). The most famous rules, typically involving counting Young tableaux, are for the most stable version, but the unstable version admits the most generalizations, to K-theory, equivariant cohomology, quantum cohomology, and to other homogeneous varieties. I'll explain how to compute the multiplication in many of these cases by counting "puzzles".
This work is joint with Terry Tao and Paul Zinn-Justin.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm,