{
  "id": "1911.02840",
  "version": "v1",
  "published": "2019-11-07T10:52:23.000Z",
  "updated": "2019-11-07T10:52:23.000Z",
  "title": "Differential Equations and Monodromy",
  "authors": [
    "Tyakal N. Venkataramana"
  ],
  "comment": "This expository paper has been accepted for publication in the Proceedings of the Telangana Academy of Sciences",
  "categories": [
    "math.CA",
    "math.GR",
    "math.HO"
  ],
  "abstract": "In these expository notes, we describe results of Cauchy, Fuchs and Pochhammer on differential equations. We then apply these results to hypergeometric differential equation of type $_nF_{n-1}$ and describe Levelt's theorem determining the monodromy representation explicitly in terms of the hypergeometric equation. We also give a brief overview, without proofs, of results of Beukers and Heckman, on the Zariski closure of the monodromy group of the hypergeometric equation. In the last section, we recall some recent results on thin-ness and arithmeticity of hypergeometric monodromy groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-07T10:52:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34M35"
    ],
    "keywords": [
      "hypergeometric equation",
      "hypergeometric differential equation",
      "hypergeometric monodromy groups",
      "levelts theorem",
      "monodromy representation"
    ],
    "tags": [
      "expository article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}