Paige Randall North

I am a Research Visiting Assistant Professor in the Mathematics Department at the Ohio State University, working with Sanjeevi Krishnan, and an Honorary Research Fellow at the University of Birmingham. Before this, I did my PhD at the University of Cambridge under the supervision of Martin Hyland. Before that, I was an undergraduate at the University of Chicago.

Research

In my research, I apply tools of topology and category theory to problems in computer science. I am most focused on homotopy type theory and univalent foundations, and I am expanding my research to include problems of rewriting.

Publications and preprints

• Type-theoretic weak factorization systems (2019). arXiv:1906.00259
• Towards a directed homotopy type theory (2019), to appear in the proceedings of the Thirty-Fifth Conference on the Mathematical Foundations of Programming Semantics (MFPS XXXV), Elsevier. arXiv:1807.10566
• Identity types and weak factorization systems in Cauchy complete categories (2019), in Mathematical Structures in Computer Science, Cambridge University Press. doi:10.1017/S0960129519000033
• Univalent foundations and the equivalence principle (2018), with Benedikt Ahrens, expository, to appear in Synthese, Springer. PDF
• Type theoretic weak factorization systems (2017), my PhD thesis. doi:0.17863/CAM.11207
• 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:10.1007/978-3-319-21284-5_16
• Some degenerate weak categories (2011), undergraduate project. PDF
• A foundational category (2010), undergraduate project. PDF

Upcoming events

• International Conference on Homotopy Type Theory, Carnegie Mellon University, 12-17 August 2019.
• Midwest Homotopy Type Theory Seminar, University of Michigan, 19-20 October 2019.

Talks

• Summer School on Higher Topos Theory and Univalent Foundations, "Homotopical models of type theory," University of Leeds, 25 June 2019.
• Homotopy Type Theory and Univalent Foundations Workshop, "Directed weak factorization systems for type theory," Senter for grunnforskning, Oslo, 14 June 2019.
• Mathematical Foundations of Programming Semantics XXXV, "Towards a directed homotopy type theory," University College London, 7 June 2019.
• 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.
• Category Theory 2018, "Directed type theory and weak factorization systems," Universidade dos Açores, 10 July 2018.
• 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.
• Conference on types for proofs and programs, "A type theory for directed homotopy theory", University of Minho, 18-21 June 2018.
• Theory Seminar, "A homotopy type theory for directed homotopy theory," University of Birmingham, 8 June 2018.
• 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.
• Joint Mathematics Meetings, "Weak factorization systems as models of dependent type theory", San Diego, 11 January 2018.
• 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.
• 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.
• 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

• Summer 2019: Type Theory
• Autumn 2018: MATH 2568 Linear Algebra
• Spring 2018: MATH 2366 Introduction to Discrete Mathematics
• Autumn 2017: MATH 2568 Linear Algebra

Organization

• Homotopy type theory seminar and reading group

Contact

north.138@osu.edu

Math Tower 514
231 West 18th Avenue
Columbus OH, 43210