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Nesta van der Schaaf.

About. My name is Nesta van der Schaaf (he/him). I'm a postdoctoral researcher at Inria Saclay, working in the QuaCS group of the Laboratoire Méthodes Formelles. I'm broadly interested in mathematical physics. The core of my research is point-free and categorical foundations of order theory. The long-term aim of this project is twofold: to provide a point-free mathematical foundation for spacetimes; and to provide a rigorous notion for concurrency in categorical quantum mechanics. I'm also interested in diffeology.
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Papers

  1. Some Results on Causal Modalities in General Spacetimes, 2026

    Preprint, arXiv:2601.14029; with Marco Lewis.

  2. Causal Coverage in Ordered Locales and Spacetimes, 2025

    Preprint, arXiv:2510.17417; with Chris Heunen.

  3. Ordered Locales, 2024

    Journal of Pure and Applied Algebra, vol. 288(7), pp. 107654; with Chris Heunen.

  4. Axioms for the category of Hilbert spaces and linear contractions, 2024

    Bulletin of the London Mathematical Society, vol. 56(4), pp. 1532-1549; with Chris Heunen and Andre Kornell.

  5. Diffeological Morita Equivalence, 2021

    Cahiers de Topologie et Géométrie Différentielle Catégoriques LXII.2 (2021), pp. 177-238.

Talks

Theses

  • Towards Point-Free Spacetimes, 2024

    PhD thesis, University of Edinburgh, supervised by Chris Heunen, 10 May 2024.

  • Diffeology, Groupoids & Morita Equivalence, 2020

    MSc thesis, Radboud University, supervised by Klaas Landsman, June 2020. Main result published as [1].

  • Classical and Quantum Particles in Galilean and Poincaré Spacetime, 2017

    BSc thesis, Radboud University, supervised by Klaas Landsman, August 2017.

Teaching

  • Tutor Adjoint School 2023

    Joint research project on concurrency in monoidal categories for the Adjoint School, part of ACT 2023.

  • Teaching assistant University of Edinburgh, 2021-2022
    • Proofs and Problem Solving
    • Introduction to Linear Algebra
    • Differentiable Manifolds (MSc)
  • Teaching assistant Radboud University, 2018-2020
    • Introduction to Mathematics, Sep.2018-Nov.2018
    • Topology, Jan.2019 - Jun.2019
    • Introduction to Mathematics, Sep.2019-Nov.2019
    • Continuous Matrix Groups, Jan.2020-Jul.2020

Employment

Education

Languages

  • Dutch native
  • English fluent
  • اُردُوelementary

Misc. notes

  • Morita Equivalence and C*-correspondences

    Literature study. Proves the characterisation of Morita equivalence of C*-algebras in terms of invertible bimodules, 2018-2020. [notes]

  • Twisted Group C*-algebras and Projective Unitary Representations

    Final project for a course on C*-algebras. Gives an overview of the characterisation of projective unitary representations of locally compact Hausdorff groups in terms of twisted group C*-algebras, January 2018. [notes]