# Nesta van der Schaaf.

PhD student in the Laboratory for Foundations of Computer Science at the University of Edinburgh with Chris Heunen. 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

Relativistic concepts in point-free spaces

(with Chris Heunen and Prakash Panangaden)

Upcoming accepted talk at Causalworlds, September 2024.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, 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.

## 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]