Nesta van der Schaaf.
Postdoctoral researcher in the QuaCS group. I'm broadly interested in mathematical physics, and currently studying causality and spacetimes using point-free topology. Also interested in category theory, foundations of (quantum) physics, and diffeology.
Contact me: <n.schaaf@ed.ac.uk>
Papers
Ordered Locales
(with Chris Heunen)
Online in JPAA, 7 March 2024.
[journal][arXiv]Axioms for the category of Hilbert spaces and linear contractions
(with Chris Heunen and Andre Kornell)
Online in BLMS, 24 February 2024.
[journal][arXiv]Diffeological Morita Equivalence
Cahiers de Topologie et Géométrie Différentielle Catégoriques LXII.2 (2021), pp. 177-238.
[journal][arXiv]
Point-free causality
To study causality in point-free topology, we use an abstraction of the Egli-Milner relation on open regions (see figure). In Ordered Locales we prove that this generalises Stone Duality to include causal orderings, hence providing a framework for point-free causal spaces. Within this framework we are developing a point-free causal boundary construction.
Talks
Causal Coverage in Ordered Locales
(with Chris Heunen)
Accepted talk at PSSL 109, 17 November 2024.
[slides]Relativistic concepts in point-free spaces
(with Chris Heunen and Prakash Panangaden)
Accepted talk at Causalworlds, 19 September 2024.
[recording]Relativistic concepts in point-free spaces
(with Chris Heunen and Prakash Panangaden)
Accepted talk at IQSA 2024, 26 July 2024.Relativistic concepts in point-free spaces
(with Chris Heunen and Prakash Panangaden)
Work-in-progress talk at Oxford Quantum Lunch, 21 March 2024.
[slides]Ordered Locales
(with Chris Heunen)
Invited talk at the Birmingham Theory Seminar, 1 March 2024.
[slides][abstract]Ordered Locales
(with Chris Heunen)
Edinburgh Category Theory Seminar, 8 November 2023.
[slides][abstract]Towards Point-Free Spacetimes
(with Chris Heunen and Prakash Panangaden)
Students in Theoretical and Mathematical Physics Seminar, 5 October 2023.
[abstract]Axioms for the category of Hilbert spaces and linear contractions
(with Chris Heunen and Andre Kornell)
Plenary talk at QPL 2023, 19 July 2023.
[slides]Ordered Locales
(with Chris Heunen)
Parallel talk at QPL 2023, 18 July 2023.
[ppt]Axioms for the category of Hilbert spaces and linear contractions
(with Chris Heunen and Andre Kornell)
Students in Theoretical and Mathematical Physics Seminar, 23 March 2023.
[slides]Axioms for the category of Hilbert spaces and linear contractions
(with Chris Heunen and Andre Kornell)
Edinburgh Category Theory Seminar, 18 January 2023.
[slides]Abstract axioms for Hilbert spaces and linear contractions
(with Chris Heunen and Andre Kornell)
Quantum Software Lab Workshop, 13 December 2022.
[event][slides][recording]Sejny Summer Institute mini-lecture series
Short lecture series on causality in point-free topology at Sejny Summer Institute, July 2022.
[slides]Diffeology, Groupoids & Morita Equivalence
Department presentation of my MSc thesis, 26 June 2020.
[slides]Lie Groupoids II
Two-part lecture series on Lie groupoids at the Radboud Noncommutative Geometry Seminar, 8 December, 2018.Lie Groupoids I
Two-part lecture series on Lie groupoids at the Radboud Noncommutative Geometry Seminar, 4 December, 2018.Twisted Group C*-algebras and Projective Unitary Representations
Lecture for final project of course on C*-algebras, January 2018.
[notes]Differentiable Stacks
Lecture for master seminar course, 23 October 2017.
[notes]Classical and Quantum Particles in Galilean and Poincaré Spacetime
Department presentation of my BSc thesis, 12 June 2017.
[slides]
Theses
Towards Point-Free Spacetimes
PhD thesis supervised by Chris Heunen, 10 May 2024.
[arXiv]Diffeologogy, Groupoids & Morita Equivalence
MSc thesis supervised by Klaas Landsman, June 2020. Main result in Cahiers de Topologie et Géométrie Différentielle Catégoriques LXII.2 (2021), pp. 177-238.
[pdf][journal]Classical and Quantum Particles in Galilean and Poincaré Spacetime
BSc thesis supervised by Klaas Landsman, August 2017.
[pdf]
Teaching
Tutor Adjoint School 2023
Joint research project on concurrency in monoidal categories for the Adjoint School, part of ACT 2023.Teaching assistant UoE, 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
Postdoctoral Researcher, QuaCS, 2024-
Education
PhD Informatics, University of Edinburgh, 2020-2024
Supervised by Chris Heunen.MSc Mathematics, Radboud University, 2017-2020
BSc Physics and Astronomy, Radboud University, 2013-2017
HBO Propedeuse Engineering Physics, Fontys Eindhoven, 2012-2013
HAVO High School, De Werkplaats Kindergemeenschap, 2007-2012
Primary School, OMS Den Dolder, 1999-2007
Languages
Dutch Native
English Fluent, Cambridge ESOL First Certificate (C1), June 2011
Urdu (اُردُو) Elementary
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]