Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 Fall 2018

Speaker:  Allen Knutson, Cornell University
Title: Segre-Schwartz-MacPherson classes and Schubert calculus
Time: 2:30 PM, Monday, September 17, 2018
Place:  Malott 206

Abstract: The most traditional version of Schubert calculus concerns the multiplication of the Schubert basis elements in the cohomology of the Grassmannian, and was given a positive formula in the 1930s. Terry Tao and I gave an extension to equivariant cohomology in 2003,which is in some ways easier because the equivariant classes satisfy a simple recurrence.

I'll explain a better recurrence that produces a better (?) set of classes, and a formula for their multiplication, again using "puzzles" as in 2003 (but this time jointly with Paul Zinn-Justin). One can take a limit to produce the old formula, breaking some of the symmetry of this better formula.

Time permitting, I'll talk about extensions beyond Grassmannians to d-step flag manifolds, and how things go bad for d>4. Even at d=4, this limit can't be taken -- the formula is fundamentally for multiplying the richer set of classes.




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