{
  "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",
    "count": 1,
    "per_page": 100,
    "pages": 1,
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  },
  "projects": [
    {
      "project_id": "OCENW.KLEIN.376",
      "title": "Scale-dependent approach to noncommutative geometry: applications to quantum physics",
      "funding_scheme_id": 4109,
      "funding_scheme": "Open Competitie ENW - M Doorlopend OC ENW KLEIN pakket 07",
      "department": "Exacte en Natuurwetenschappen",
      "sub_department": "Exacte en Natuurwetenschappen",
      "start_date": "2021-09-01T00:00:00",
      "end_date": "2025-08-31T00:00:00",
      "reporting_year": 2020,
      "summary_nl": "In the first part of this project we intend to develop a formalism for truncated spectral geometry. Thus, we will deal with the question ``can one hear the shape of a drum'' asked by mathematician Mark Kac in 1966 in the case that we only have the part of the spectrum of, say, a Laplacian available. The main question is then whether and how we approximate the original geometric space by taking into account larger and larger parts of the spectrum, corresponding to smaller and smaller length scales.  \n\n\n\nWe will work in the natural and more general context of noncommutative geometry where we will be dealing with spectra of self-adjoint operators. We will develop a formalism to deal with truncations of this structure, typically involving a spectral projection of some self-adjoint ``Dirac'' operator D--- essentially a square-root of a Laplacian. This forces us to replace C*-algebras by operator systems. So, even though we loose the algebraic structure, we still have sufficient structure to talk about state spaces. Indeed, states (as positive normalized functionals) makes sense for operator systems. Moreover, one may define a distance formula on the state space for such truncated systems which we intend to analyze in this proposal. In particular, it forms the basis for the type of Gromov-Hausdorff convergence that we intend to use to make the aforementioned approximation mathematically precise.\n\n\n\n\n\nIn the second part of the project we will apply our formalism to include quantum corrections to the spectral description of geometry. At small scales (large frequencies) it is well-known that there are quantum field theoretic corrections to the propagation of a particle. This motivates us to replace the Dirac operator (as the inverse propagator) by a dressed Dirac operator, so as to take into account these quantum corrections. The resulting operator is not a first-order operator any more, hence more difficult to analyze. However, by working in the formalism of truncated spectral geometry just developed we will still be able to study the effect quantum field theory has on geometry at the small scale. As an example, we will determine the dimension spectrum of the space, as well as the distance function, in terms of the truncated operator. As a result, we will arrive at a description of quantum theory at the purely geometric level.",
      "summary_en": "In the first part of this project we intend to develop a formalism for truncated spectral geometry. Thus, we will deal with the question ``can one hear the shape of a drum'' asked by mathematician Mark Kac in 1966 in the case that we only have the part of the spectrum of, say, a Laplacian available. The main question is then whether and how we approximate the original geometric space by taking into account larger and larger parts of the spectrum, corresponding to smaller and smaller length scales.  \n\n\n\nWe will work in the natural and more general context of noncommutative geometry where we will be dealing with spectra of self-adjoint operators. We will develop a formalism to deal with truncations of this structure, typically involving a spectral projection of some self-adjoint ``Dirac'' operator D--- essentially a square-root of a Laplacian. This forces us to replace C*-algebras by operator systems. So, even though we loose the algebraic structure, we still have sufficient structure to talk about state spaces. Indeed, states (as positive normalized functionals) makes sense for operator systems. Moreover, one may define a distance formula on the state space for such truncated systems which we intend to analyze in this proposal. In particular, it forms the basis for the type of Gromov-Hausdorff convergence that we intend to use to make the aforementioned approximation mathematically precise.\n\n\n\n\n\nIn the second part of the project we will apply our formalism to include quantum corrections to the spectral description of geometry. At small scales (large frequencies) it is well-known that there are quantum field theoretic corrections to the propagation of a particle. This motivates us to replace the Dirac operator (as the inverse propagator) by a dressed Dirac operator, so as to take into account these quantum corrections. The resulting operator is not a first-order operator any more, hence more difficult to analyze. However, by working in the formalism of truncated spectral geometry just developed we will still be able to study the effect quantum field theory has on geometry at the small scale. As an example, we will determine the dimension spectrum of the space, as well as the distance function, in terms of the truncated operator. As a result, we will arrive at a description of quantum theory at the purely geometric level.",
      "award_amount": 259970,
      "grant_id": "https://doi.org/10.61686/JRFXD01970",
      "project_members": [
        {
          "role": "Researcher",
          "member_id": 493304,
          "last_name": "Leimbach",
          "initials": "M.",
          "first_name": "Malte",
          "organisation": "Radboud Universiteit Nijmegen||Faculteit der Natuurwetenschappen, Wiskunde en Informatica||Institute for Mathematics, Astrophysics and Particle Physics (IMAPP)",
          "organisation_id": 73889,
          "ror": "https://ror.org/016xsfp80",
          "active": false
        },
        {
          "role": "Main Applicant",
          "member_id": 130274,
          "last_name": "Suijlekom",
          "degree_pre_nominal": "prof. dr.",
          "initials": "W.D.",
          "first_name": "Walter",
          "prefix": "van",
          "organisation": "Radboud Universiteit Nijmegen||Faculteit der Natuurwetenschappen, Wiskunde en Informatica||Institute for Mathematics, Astrophysics and Particle Physics (IMAPP)",
          "organisation_id": 73889,
          "ror": "https://ror.org/016xsfp80",
          "active": true
        },
        {
          "role": "Project leader",
          "member_id": 130274,
          "last_name": "Suijlekom",
          "degree_pre_nominal": "prof. dr.",
          "initials": "W.D.",
          "first_name": "Walter",
          "prefix": "van",
          "organisation": "Radboud Universiteit Nijmegen||Faculteit der Natuurwetenschappen, Wiskunde en Informatica||Subfaculteit Wiskunde",
          "organisation_id": 77719,
          "ror": "https://ror.org/016xsfp80",
          "active": true
        }
      ]
    }
  ]
}