{
  "id": "math/0507377",
  "version": "v2",
  "published": "2005-07-19T19:15:33.000Z",
  "updated": "2005-11-22T12:11:28.000Z",
  "title": "Experimentation and conjectures in the real Schubert calculus for flag manifolds",
  "authors": [
    "James Ruffo",
    "Yuval Sivan",
    "Evgenia Soprunova",
    "Frank Sottile"
  ],
  "comment": "34 pages. Revised and one example removed. Expanded version of math.AG/0502040. Related WWW page http://www.math.tamu.edu/~sottile/pages/Flags/index.html",
  "journal": "Experimental Mathematics, 15, No. 2 (2006), 199--221.",
  "categories": [
    "math.AG"
  ],
  "abstract": "The Shapiro conjecture in the real Schubert calculus, while likely true for Grassmannians, fails to hold for flag manifolds, but in a very interesting way. We give a refinement of the Shapiro conjecture for the flag manifold and present massive (15.76 gigahertz-years) computational experimentation in support of this refined conjecture. We also prove the conjecture in some special cases using discriminants and establish relationships between different cases of the conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-11-22T12:11:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N15",
      "14P99",
      "12D10"
    ],
    "keywords": [
      "real schubert calculus",
      "flag manifold",
      "shapiro conjecture",
      "computational experimentation",
      "special cases"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7377R"
    }
  }
}