Experimentation in the Schubert Calculus
arXiv:1308.3284
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.
30 pages. Based on Sottile's talks at 2012 MSJ-SI on Schubert Calculus