{
  "id": "2110.07533",
  "version": "v2",
  "published": "2021-10-14T16:52:28.000Z",
  "updated": "2022-08-23T22:45:33.000Z",
  "title": "Uniformization of some weight 3 variations of Hodge structure, Anosov representations, and Lyapunov exponents",
  "authors": [
    "Simion Filip"
  ],
  "comment": "improved exposition; 103 pages, 3 tables, 5 figures",
  "categories": [
    "math.AG",
    "math.CA",
    "math.DS",
    "math.GT"
  ],
  "abstract": "We develop a class of uniformizations for certain weight 3 variations of Hodge structure (VHS). The analytic properties of the VHS are used to establish a conjecture of Eskin, Kontsevich, M\\\"oller, and Zorich on Lyapunov exponents. Additionally, we prove that the monodromy representations are log-Anosov, a dynamical property that has a number of global consequences for the VHS. We establish a strong Torelli theorem for the VHS and describe appropriate domains of discontinuity. Additionally, we classify the hypergeometric differential equations that satisfy our assumptions. We obtain several multi-parameter families of equations, which include the mirror quintic as well as the six other thin cases of Doran--Morgan and Brav--Thomas.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-08-23T22:45:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D07",
      "34D08",
      "33C20",
      "37D20",
      "14C34"
    ],
    "keywords": [
      "hodge structure",
      "lyapunov exponents",
      "anosov representations",
      "uniformization",
      "variations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 103,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}