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.

**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]

**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]

- 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. -
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.

- 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)

- TYPES (steering committee member)
- ACT 2022 (pc member)
- HoTT/UF 2022 (organizer)
- Homotopy type theory reading group, Autumn 2020
- Fourth Midwest HoTT Seminar (organizer), postponed.
- Homotopy type theory seminar and reading group, Autumn 2017 - Spring 2018

Hans Freudenthalgebouw 6.05

Budapestlaan 6

3584 CD Utrecht

Buys Ballotgebouw 5.65

Princetonplein 5

3584 CC Utrecht