## Advanced Studies in Pure Mathematics

### Schubert calculus and puzzles

Allen Knutson

#### Abstract

These are notes for four lectures given at the Osaka summer school on Schubert calculus in 2012, presenting the geometry from the unpublished arXiv:1008.4302 giving an extension of the puzzle rule for Schubert calculus to equivariant $K$-theory, while eliding some of the combinatorial detail. In particular, §3 includes background material on equivariant cohomology and $K$-theory.

Since that school, I have extended the results to arbitrary interval positroid varieties (not just those arising in Vakil's geometric Littlewood-Richardson rule), in the preprint [Kn2].

#### Article information

Dates
Received: 23 August 2013
Revised: 1 October 2014
First available in Project Euclid: 4 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538623000

Digital Object Identifier
doi:10.2969/aspm/07110185

Mathematical Reviews number (MathSciNet)
MR3644824

Zentralblatt MATH identifier
1378.14055

#### Citation

Knutson, Allen. Schubert calculus and puzzles. Schubert Calculus — Osaka 2012, 185--209, Mathematical Society of Japan, Tokyo, Japan, 2016. doi:10.2969/aspm/07110185. https://projecteuclid.org/euclid.aspm/1538623000