{
  "meta": {
    "api_type": "NWO Projects API",
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    "licence": {
      "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",
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  "projects": [
    {
      "project_id": "613.009.152",
      "title": "Solvable quantum knot invariants",
      "funding_scheme_id": 4033,
      "funding_scheme": "Wiskundeclusters (rondes vanaf 2016) Wiskundeclusters PhD-posities 2019",
      "department": "Exacte en Natuurwetenschappen",
      "sub_department": "Exacte en Natuurwetenschappen",
      "start_date": "2021-11-01T00:00:00",
      "reporting_year": 2020,
      "summary_nl": "Ideas from quantum field theory and integrable systems have revolutionized the area of low-\n\ndimensional topology, as witnessed by the Fields medals of Jones, Witten and Drinfeld\n\nin 1990. Powerful new methods of distinguishing knots and 3-manifolds known as quantum invariants\n\nwere developed and some long standing conjectures were solved quickly. Thirty years later the quan-\n\ntum invariants have been refined and are firmly anchored in various mathematical frameworks. However for solving actual problems in topology the quantum invariants have not yet delivered on their promise.\n\n\n\nPart of the problem of applying quantum invariants is that the number of terms involved grows\n\nexponentially in the complexity of the knot. This also makes it very hard to prove any properties of\n\ntopological interest. Recently Bar-Natan and van der Veen found a new approach to quantum\n\ninvariants using solvable approximations to quantum groups. The resulting solvable quantum invariants\n\nare much easier to work with while remaining sufficiently powerful to distinguish subtle topological\n\nfeatures. The goal of this project is to explore the solvable quantum invariants in two ways: Making contact\n\nwith the loop expansion of the colored Jones polynomial and attacking the long standing slice-ribbon conjecture in topology.\n\n\n\nTwo key innovations in this proposal are the solvable approximations and Gaussian generating functions. Modifying the Drinfeld double construction, the quantized enveloping algebras of semi-simple Lie algebras can be approached by a family of simpler Drinfeld doubles depending on a parameter. Second we use a PBW basis to normal-order all our expressions and pull back all maps to a commutative setting. Here all expressions and operations can be summarized by generating functions that form a category. The solvable approximation implies that all generating functions in the category are perturbed Gaussians. Such Gaussians are amenable to methods of quantum field theory.",
      "summary_en": "Ideas from quantum field theory and integrable systems have revolutionized the area of low-\n\ndimensional topology, as witnessed by the Fields medals of Jones, Witten and Drinfeld\n\nin 1990. Powerful new methods of distinguishing knots and 3-manifolds known as quantum invariants\n\nwere developed and some long standing conjectures were solved quickly. Thirty years later the quan-\n\ntum invariants have been refined and are firmly anchored in various mathematical frameworks. However for solving actual problems in topology the quantum invariants have not yet delivered on their promise.\n\n\n\nPart of the problem of applying quantum invariants is that the number of terms involved grows\n\nexponentially in the complexity of the knot. This also makes it very hard to prove any properties of\n\ntopological interest. Recently Bar-Natan and van der Veen found a new approach to quantum\n\ninvariants using solvable approximations to quantum groups. The resulting solvable quantum invariants\n\nare much easier to work with while remaining sufficiently powerful to distinguish subtle topological\n\nfeatures. The goal of this project is to explore the solvable quantum invariants in two ways: Making contact\n\nwith the loop expansion of the colored Jones polynomial and attacking the long standing slice-ribbon conjecture in topology.\n\n\n\nTwo key innovations in this proposal are the solvable approximations and Gaussian generating functions. Modifying the Drinfeld double construction, the quantized enveloping algebras of semi-simple Lie algebras can be approached by a family of simpler Drinfeld doubles depending on a parameter. Second we use a PBW basis to normal-order all our expressions and pull back all maps to a commutative setting. Here all expressions and operations can be summarized by generating functions that form a category. The solvable approximation implies that all generating functions in the category are perturbed Gaussians. Such Gaussians are amenable to methods of quantum field theory.",
      "award_amount": 199976,
      "grant_id": "https://doi.org/10.61686/WHENI49237",
      "project_members": [
        {
          "role": "Researcher",
          "member_id": 503312,
          "last_name": "Bosch",
          "initials": "B. J.",
          "first_name": "Boudewijn",
          "organisation": "Rijksuniversiteit Groningen",
          "organisation_id": 7905,
          "ror": "https://ror.org/012p63287",
          "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": "Rijksuniversiteit Groningen||Faculty of Science and Engineering (FSE)||Bernoulli Institute for Mathematics Computer Science and Artificial Intelligence",
          "organisation_id": 72806,
          "ror": "https://ror.org/012p63287",
          "active": true
        },
        {
          "role": "Project leader",
          "member_id": 166399,
          "last_name": "Veen",
          "degree_pre_nominal": "dr.",
          "initials": "R.I.",
          "first_name": "Roland",
          "prefix": "van der",
          "organisation": "Rijksuniversiteit Groningen||Faculty of Science and Engineering (FSE)||Bernoulli Institute for Mathematics Computer Science and Artificial Intelligence",
          "organisation_id": 72806,
          "ror": "https://ror.org/012p63287",
          "active": true
        }
      ]
    }
  ]
}