Advanced Studies in Pure Mathematics

Experimentation in the Schubert Calculus

Abraham Martín del Campo and Frank Sottile

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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


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