Paige Randall North
I am an assistant professor at Utrecht University with a dual appointment in the Department of Mathematics and the Department of Information and Computing Sciences. I am also an Honorary Research Fellow in the School of Computer Science at the University of Birmingham and a Guest Researcher at the Delft University of Technology.
Previously, I was a postdoc in the Departments of Mathematics and Electrical and Systems Engineering at the University of Pennsylvania, working with Rob Ghrist, and in the Mathematics Department at the Ohio State University, working with Sanjeevi Krishnan.
Before that, I did my PhD in mathematics at the University of Cambridge under the supervision of Martin Hyland, and my BS in mathematics at the University of Chicago.
In my research, I apply tools of topology and category theory to problems in computer science. I am most focused on the connections between type theory and homotopy theory/higher category theory.
Publications
- Semantics for two-dimensional type theory (2022), joint with B. Ahrens and N. van der Weide, to appear in Proceedings of the Thirty-Seventh Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). [arXiv]
- A Hurewicz model structure for directed topology (2021), joint with S. Krishnan,
in Theory and Applications of Categories, Vol. 37, No. 20, pp 613-634. [tac][arXiv]
- A higher structure identity principle (2020), joint with B. Ahrens, M. Shulman, D. Tsementzis, in Proceedings of the Thirty-Fifth Annual ACM/IEEE Symposium on
Logic in Computer Science (LICS). [doi][arXiv]
- Towards a directed homotopy type theory (2019), in Proceedings of the Thirty-Fifth Conference on the Mathematical Foundations of Programming Semantics (MFPS), Electronic Notes in Theoretical Computer Science. [doi][arXiv]
- Identity types and weak factorization systems in Cauchy complete categories (2019), in Mathematical Structures in Computer Science. [doi][arXiv]
- Univalent foundations and the equivalence principle (2019), joint with with B. Ahrens, expository, in Reflections on the Foundations of Mathematics, Synthese. [doi][pdf]
Preprints
- B-systems and C-systems are equivalent (2021), joint with B. Ahrens, J. Emmenegger, and E. Rijke. [arXiv]
- The univalence principle (2021), joint with B. Ahrens, M. Shulman, D. Tsementzis, submitted. [arXiv]
- Type-theoretic weak factorization systems (2019), submitted. [arXiv]
Other writings
- Type theory (2019), lecture notes taken by Jason Schuchardt during my course on Type Theory at the Ross Program. [pdf]
- Type theoretic weak factorization systems (2017), my PhD thesis. [doi]
- Towards a Topological Model of Homotopy Type Theory (2015), In: González M., Yang P., Gambino N., Kock J. (eds) Extended Abstracts Fall 2013. Trends in Mathematics. Birkhäuser, Cham. [doi]
- Some degenerate weak categories (2011), undergraduate project. [pdf]
- A foundational category (2010), undergraduate project. [pdf]
Talks
- 11th International Conference on Geometric and Topological Methods in Computer Science (GETCO), Directed homotopy type theory, École pour l'informatique et les techniques avancées (EPITA), 3 June 2022. [slides] [video]
- Dutch Categories And Types Seminar Workshop on Algebraic Weak Factorisation Systems, Two-sided and other generalizations of weak factorization systems, Universiteit van Amsterdam, 2 May 2022. [slides] [video]
- Socio-Math Miniworkshop, A categorical perspective on opinion dynamics, Basic Research Office of the Department of Defense, 11 April 2022. [slides]
- North American Annual Meeting of the Association for Symbolic Logic (ASL), The univalence principle, Cornell University, 10 April 2022. [slides]
- "An introduction to homotopy type theory and univalent foundations" Miniseries, An introduction to univalent foundations and the equivalence principle, Max Planck Institute for Mathematics in Bonn, 28 March 2022. [slides]
- Logic and Computation Seminar, The Univalence Principle (a series of 3 talks), University of Pennsylvania, 13-27 September 2021. [slides for talk 1, 2, 3]
- Minisymposium on Physically Grounded Semantics for Programming Hybrid Dynamical Systems, Directed type theory for state space analysis SIAM 2021 Conference on Control Theory, 21 July 2021. [video] [slides]
- Laboratory for Foundations of Computer Science Seminar, Directed homotopy type theory, University of Edinburgh, 1 June 2021. [slides]
- Workshop on Semantics of Type Theory, B- and E-systems, Univerza v Ljubljani, 20 May 2021.
- Homotopy theory seminar, The univalence principle, Florida State University, 27 April 2021. [slides]
- Spring School on Theoretical Computer Science (EPIT) – Homotopy Type Theory, Directed homotopy type theory, L’Institut national de recherche en informatique et en automatique (INRIA) et le Centre national de la recherche scientifique (CNRS), 16 April 2021. [video]
- Kod*lab Robotics Seminar, Introduction to homotopy type theory and future applications, University of Pennsylvania, 30 March 2021.
- Algebra | Coalgebra Seminar, The univalence principle, Institute for Language, Logic and Computation, Universiteit van Amsterdam, 2 December 2020. [slides]
- Radical π Seminar, Easier math in a computer, Ohio State University, 18 November 2020.
- Pizza Seminar, Univalent foundations and the equivalence principle, University of Pennsylvania, 16 October 2020. [slides]
- Thirty-Fifth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), A Higher Structure Identity Principle, 10 July 2020. [slides][video]
- Homotopy type theory electronic seminar talks (HoTTEST) Conference, A Higher Structure Identity Principle, University of Western Ontario, 17 June 2020. [slides][video]
- Foundations and Applications of Univalent Mathematics, Two-sided Weak Factorization Systems for Directed Type Theory, Ludwig-Maximilians-Universität München, 18 December 2019. [slides]
- Applied topology seminar, Type theory and directed homotopy theory, University of Pennsylvania, 3 December 2019. [slides]
- Midwest Homotopy Type Theory Seminar, Two-sided weak factorization systems, University of Michigan, 20 October 2019. [slides]
- Visiting lecture, Directed type theory and homotopy theory, Aarhus universitet, 10 October 2019. [slides]
- Logic seminar, Two-sided weak factorization systems, Stockholms universitet, 2 October 2019. [slides]
- International Conference on Homotopy Type Theory, A higher structure identity principle, Carnegie Mellon University, 13 August 2019. [slides]
- Summer School on Higher Topos Theory and Univalent Foundations, Homotopical models of type theory, University of Leeds, 25 June 2019. [slides]
- Homotopy Type Theory and Univalent Foundations Workshop, Directed weak factorization systems for type theory, Senter for grunnforskning, Oslo, 14 June 2019. [slides]
- Mathematical Foundations of Programming Semantics (MFPS) XXXV, Towards a directed homotopy type theory, University College London, 7 June 2019. [slides]
- Sixth Workshop on Formal Topology, Constructing models of homotopy type theory with abstract real numbers, University of Birmingham, 12 April 2019.
- Homotopy Type Theory and Univalent Foundations Seminar, Directed weak factorization systems and type theories, Senter for grunnforskning, Oslo, 21 January 2019. [slides]
- Category Theory 2018, Directed type theory and weak factorization systems, Universidade dos Açores, 10 July 2018. [slides]
- Workshops on Homotopy Type Theory/Univalent Foundations and Higher-Dimensional Rewriting and Algebra, A homotopy type theory for directed homotopy theory, University of Oxford, 7 July 2018. [slides]
- Conference on types for proofs and programs, A type theory for directed homotopy theory, University of Minho, 18-21 June 2018. [slides]
- Theory Seminar, A homotopy type theory for directed homotopy theory, University of Birmingham, 8 June 2018. [slides]
- Midwestern HoTT Seminar, A directed homotopy type theory, University of Western Ontario, 26 May 2018.
- AMS Spring Central Sectional Meeting, Type theory and concurrency, Ohio State University, 17 March 2018. [slides]
- Joint Mathematics Meetings, Weak factorization systems as models of dependent type theory, San Diego, 11 January 2018. [slides]
- Welcome Seminar, Type theory and homotopy theory, Ohio State University, 30 November 2017.
- Category Theory Octoberfest, Comprehension categories and weak factorization systems, Carnegie Mellon University, 28 October 2017
- Topology Seminar, An introduction to the relationship between type theory and homotopy theory, Ohio State University, 17 October 2017.
- Stockholm Logic Seminar, Weak factorization systems and display map categories, Stockholms universitet, 5 April 2017.
- EUTypes meeting, Categories of display map categories, Univerza v Ljubljani, 31 January 2017.
- Foundations of Mathematics: Univalent Foundations and Set Theory, Models of Type Theory, Zentrum für interdisziplinäre Forschung, Bielefeld, 20 July 2016.
- Workshop on Homotopy Type Theory and Univalent Foundations of Mathematics, Topological models of dependent type theory, The Fields Institute, Toronto, 20 May 2016.
- Categorical homotopy theory lecture series, Capital Normal University, Beijing, 29 June - 3 July 2015.
- Category Theory 2015, Weak factorization systems for intensional type theory, University of Aveiro, 19 June 2015.
- Fifth Workshop on Formal Topology, Weak factorization systems for intensional type theory, Institut Mittag-Leffler, Stockholm, 9 June 2015.
- Category Theory Seminar, Weak factorization systems for intensional type theory, University of Cambridge, 12 May 2015.
- PSSL 96, Moore factorization systems, Universita degli Studi di Palermo, 12 October 2014.
- Junior Category Theory Seminar, Moore factorization systems, University of Cambridge, 9 October 2014.
- Category Theory 2014, Moore factorization systems, University of Cambridge, 4 July 2014.
- Junior Category Theory Seminar, Homotopy type theory and weak factorization systems, University of Cambridge, 6 March 2014.
- Category Theory Seminar, Towards a topological model of homotopy type theory, University of Cambridge, 26 November 2013.
- Conference on Type Theory, Homotopy Theory and Univalent Foundations, Towards a model of homotopy type theory in topological spaces, Centre de Recerca Matemàtica, Barcelona, 23 September 2013.
- Young Researchers in Mathematics, Model category theory and homotopy type theory, University of Edinburgh, 17 June 2013.
- Young Women in Topology, A framework for constructive homotopy theory, Universität Bonn, 8 June 2013.
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Joint Category Theory and Computer Science Seminar, Computational homotopy theory, University of Cambridge, 30 May 2013.
- Junior Category Theory Seminar, Model categories, University of Cambridge, 31 January 2013.
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Algebraic Topology and Category Theory Proseminar, Batanin ω-categories, University of Chicago, 22 November 2011.
- Graduate Student Conference in Logic, Univalent foundations of mathematics, University of Illinois at Chicago, 8 May 2011.
Teaching
- Autumn 2021: Calculus III -- linear algebra (Penn)
- Spring 2021: Calculus IV -- applied partial differential equations (Penn)
- Summer 2020: Applied category theory school
- Spring 2020: Foundations of Higher Mathematics (OSU) [videos]
- Summer 2019: Type Theory (Ross Program)
- Autumn 2018: Linear Algebra (OSU)
- Spring 2018: Introduction to Discrete Mathematics (OSU)
- Autumn 2017: Linear Algebra (OSU)
- Lent 2015: Number Fields (Cambridge)
- Michaelmas 2014: Galois Theory (Cambridge)
- Michaelmas 2012: Number Theory (Cambridge)
Service
Contact
p.r.north@uu.nl
Hans Freudenthalgebouw 6.05
Budapestlaan 6
3584 CD Utrecht
Buys Ballotgebouw 5.65
Princetonplein 5
3584 CC Utrecht