## 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), 295 - 335

### Experimentation in the Schubert Calculus

Abraham Martín del Campo and Frank Sottile

#### Abstract

Many aspects of Schubert calculus are easily modeled on a computer. This enables large-scale experimentation to investigate subtle and ill-understood phenomena in the Schubert calculus. A well-known web of conjectures and results in the real Schubert calculus has been inspired by this continuing experimentation. A similarly rich story concerning intrinsic structure, or Galois groups, of Schubert problems is also beginning to emerge from experimentation. This showcases new possibilities for the use of computers in mathematical research.

#### Article information

**Source***Schubert Calculus — Osaka 2012*, H. Naruse, T. Ikeda, M. Masuda and T. Tanisaki, eds. (Tokyo: Mathematical Society of Japan, 2016), 295-335

**Dates**

Received: 15 August 2013

Revised: 25 April 2014

First available in Project Euclid:
4 October 2018

**Permanent link to this document**

https://projecteuclid.org/
euclid.aspm/1538623004

**Digital Object Identifier**

doi:10.2969/aspm/07110295

**Mathematical Reviews number (MathSciNet)**

MR3644828

**Zentralblatt MATH identifier**

1378.14056

**Subjects**

Primary: 14N15: Classical problems, Schubert calculus 14P99: None of the above, but in this section

**Keywords**

Galois groups Schubert calculus Shapiro Conjecture Enumerative geometry

#### Citation

del Campo, Abraham Martín; Sottile, Frank. Experimentation in the Schubert Calculus. Schubert Calculus — Osaka 2012, 295--335, Mathematical Society of Japan, Tokyo, Japan, 2016. doi:10.2969/aspm/07110295. https://projecteuclid.org/euclid.aspm/1538623004