## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Schubert Calculus — Osaka 2012, H. Naruse, T. Ikeda, M. Masuda and T. Tanisaki, eds. (Tokyo: Mathematical Society of Japan, 2016), 185 - 209

### Schubert calculus and puzzles

#### 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notes for four lectures given at the Osaka summer school on Schubert calculus in 2012, presenting the geometry from the unpublished arXiv:1008.4302 giving an extension of the puzzle rule for Schubert calculus to equivariant $K$-theory, while eliding some of the combinatorial detail.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

**Source***Schubert Calculus — Osaka 2012*, H. Naruse, T. Ikeda, M. Masuda and T. Tanisaki, eds. (Tokyo: Mathematical Society of Japan, 2016), 185-209

**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