{
  "meta": {
    "api_type": "NWO Projects API",
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      "name": "CC0 1.0 Universal",
      "url": "https://creativecommons.org/publicdomain/zero/1.0",
      "description": "To the extent possible under law, all copyright and related or neighbouring rights have been waived worldwide to the data made available through this API."
    },
    "documentation": "https://doi.org/10.5281/zenodo.14918287",
    "release_date": "2025-08-20T00:00:00",
    "funder": "https://doi.org/10.13039/501100003246",
    "ror_id": "https://ror.org/04jsz6e67",
    "date": "2026-11-05T00:00:00",
    "count": 1,
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  "projects": [
    {
      "project_id": "639.031.242",
      "title": "Geometry of quantum knot invariants",
      "funding_scheme_id": 421,
      "funding_scheme": "NWO-Talentprogramma Veni 2012 EW",
      "department": "Exacte en Natuurwetenschappen",
      "sub_department": "Exacte Wetenschappen",
      "start_date": "2013-01-01T00:00:00",
      "end_date": "2016-12-31T00:00:00",
      "reporting_year": 2012,
      "summary_nl": "We propose to bring together two radically different ways of studying knots. According to the first viewpoint one considers the knot as a quantum system of interacting particles. Expectation values of such a system give rise to the quantum invariants of which the Jones polynomial is the best known example. Although very successful, these invariants are poorly understood and have many mysterious connections to other parts of mathematics and physics.\n\nThe second way to look at knots is to focus on the space around the knot, the knot complement. It follows from the geometrization program, recently completed by G. Perelman, that it is always possible to find an optimal geometry on a knot complement. Geometric characteristics such as the volume can thus be used to understand the knot.\n\nUnification of these two viewpoints of knot theory is an important mathematical challenge that contains several essential features of the much more complicated task of unifying general relativity and quantum mechanics. Introducing geometric structures into the study of quantum knot invariants will moreover help explain the mysterious connections to number theory and the geometric Langlands program.",
      "summary_en": "We propose to bring together two radically different ways of studying knots. According to the first viewpoint one considers the knot as a quantum system of interacting particles. Expectation values of such a system give rise to the quantum invariants of which the Jones polynomial is the best known example. Although very successful, these invariants are poorly understood and have many mysterious connections to other parts of mathematics and physics.\n\nThe second way to look at knots is to focus on the space around the knot, the knot complement. It follows from the geometrization program, recently completed by G. Perelman, that it is always possible to find an optimal geometry on a knot complement. Geometric characteristics such as the volume can thus be used to understand the knot.\n\nUnification of these two viewpoints of knot theory is an important mathematical challenge that contains several essential features of the much more complicated task of unifying general relativity and quantum mechanics. Introducing geometric structures into the study of quantum knot invariants will moreover help explain the mysterious connections to number theory and the geometric Langlands program.",
      "project_members": [
        {
          "role": "Researcher",
          "member_id": 166399,
          "last_name": "Veen",
          "degree_pre_nominal": "dr.",
          "initials": "R.I.",
          "first_name": "Roland",
          "prefix": "van der",
          "organisation": "Universiteit Leiden||Faculteit der Wiskunde en Natuurwetenschappen||Mathematisch Instituut",
          "organisation_id": 74939,
          "ror": "https://ror.org/027bh9e22",
          "active": false
        },
        {
          "role": "Project leader",
          "member_id": 166399,
          "last_name": "Veen",
          "degree_pre_nominal": "dr.",
          "initials": "R.I.",
          "first_name": "Roland",
          "prefix": "van der",
          "organisation": "Universiteit van Amsterdam||Faculteit der Natuurwetenschappen, Wiskunde en Informatica (Faculty of Science)||Korteweg-de Vries Instituut voor de Wiskunde",
          "organisation_id": 78101,
          "ror": "https://ror.org/04dkp9463",
          "active": false
        },
        {
          "role": "Researcher",
          "member_id": 166399,
          "last_name": "Veen",
          "degree_pre_nominal": "dr.",
          "initials": "R.I.",
          "first_name": "Roland",
          "prefix": "van der",
          "organisation": "Universiteit van Amsterdam||Faculteit der Natuurwetenschappen, Wiskunde en Informatica (Faculty of Science)||Korteweg-de Vries Instituut voor de Wiskunde",
          "organisation_id": 78101,
          "ror": "https://ror.org/04dkp9463",
          "active": false
        },
        {
          "role": "Main Applicant",
          "member_id": 166399,
          "last_name": "Veen",
          "degree_pre_nominal": "dr.",
          "initials": "R.I.",
          "first_name": "Roland",
          "prefix": "van der",
          "organisation": "Universiteit van Amsterdam||Faculteit der Natuurwetenschappen, Wiskunde en Informatica (Faculty of Science)||Korteweg-de Vries Instituut voor de Wiskunde",
          "organisation_id": 78101,
          "ror": "https://ror.org/04dkp9463",
          "active": true
        }
      ]
    }
  ]
}