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Research interests
My current research focus is on the safety and security of machine learning algorithms and autonomous systems. See my LinkedIn page for more details of what I've been up to recently.
My earlier research was is in algebra (category theory and homotopical algebra),
logic (categorical logic and type theory), and
mathematical foundations of computer science (logic in CS and formal
verification).
Research
Below you will find, organized roughly by research area, an assortment of links to my papers, preprints and other notes. Preprint versions may differ from journal versions.Category Theory and Homotopical Algebra
- Bicategorical fibration structures and stacks, with Dorette Pronk, Theory and Applications of Categories, 29(29), pp. 836-873, 2014.
- Model structures from a monad on presheaves, preprint, 2013.
- A characterization of representable intervals, Theory and Applications of Categories, 26(8), pp. 204-232, 2012. Preprint on the arXiv.
Type Theory
- The local universes model: an overlooked coherence construction for dependent type theories, with Peter LeFanu Lumsdaine, ACM Transactions on Computational Logic, 2015. Preprint on the arXiv.
- A univalent formalization of the p-adic numbers, with Álvaro Pelayo and Vladimir Voevodsky, Mathematical Structures in Comptuer Science, 2015. Coq code is available here.
- Homotopy type theory, with Álvaro Pelayo, Gazette des Mathématiciens, no. 142, 95-110, October, 2014.
- Voevodsky's Univalence Axiom in homotopy type theory, with Steve Awodey and Álvaro Pelayo, Notices of the American Mathematical Society, 60(08), 1164-1167, October, 2013.
- Homotopy type theory and Voevodsky's univalent foundations, with Álvaro Pelayo, Bulletin of the American Mathematical Society, 51, 597-648, 2014. Associated Coq code is available here.
- Combinatorial realizability models of type theory, with Pieter Hofstra, Annals of Pure and Applied Logic, 164(10), pp. 957-988, 2013. Preprint available on the arXiv.
- Martin-Löf Complexes, with Steve Awodey and Pieter Hofstra, Annals of Pure and Applied Logic, 164(10), pp. 928-956, 2013. Preprint available on the arXiv.
- The strict ω-groupoid interpretation of type theory, in Models, Logics and Higher-Dimensional Categories, CRM Proc. Lecture Notes 53, Amer. Math. Soc., 291-340, 2011.
- A combinatorial realizability model of 1-truncated type theory, in Oberwolfach Reports 11/2011, pp. 630-633, 2011. Available here.
- Homotopy theoretic models of identity types, with Steve Awodey, Mathematical Proceedings of the Cambridge Philosophical Society, 146, pp. 45-55, 2009. Preprint available on the arXiv.
- Homotopy theoretic aspects of constructive type theory, Ph.D. Thesis in Logic, Carnegie Mellon University, 2008.
- Homotopy models of intensional type theory, Ph.D. Thesis Prospectus, 2006.
Machine Learning, Control Theory, and Dynamical Systems
- CDOPS: Complex Dynamics of Online Professional Squads, with Brianna Duffy, Jonathan Gallagher, Jocelyn Rego, and Wael Fatnassi, IEEE Conference on Games, 2025.
- Provably effective detection of effective data poisoning attacks, with Jonathan Gallagher, Yasaman Esfandiari, and Callen MacPhee, preprint, 2025.
- Self-Satisfied: An end-to-end framework for SAT generation and prediction, with Christopher R. Serrano, Jonathan Gallagher, Kenji Yamada, and Alexei Kopylov, preprint, 2024.
- Assured Point Cloud Perception, with Christopher R. Serrano and Aleksey Nogin, IEEE International Conference on Assured Autonomy (ICAA), 2023.
- Formal Verification of octorotor flight envelope using barrier functions and satisfiability modulo theories solving, with Byron Heersink and Pape Sylla, IEEE Control Systems Letters, vol. 6, pp. 1507-1512, 2022. Preprint available here.
- Formally Verified Safety Net for Waypoint Navigation Neural Network Controllers, with Alexei Kopylov, Stefan Mitsch, and Aleksey Nogin, Formal Methods, 2021.
- Dynamic mode decomposition for interconnected control systems, with Byron Heersink and Heiko Hoffmann, preprint, 2017.
- RTA3: A real time adversarial attack on recurrent neural networks, with Chris Serrano, Pape Sylla and Sicun Gao, IEEE SPW (Deep Learning Security), 2020.
- Generate and Verify: Semantically meaningful formal analysis of neural network perception systems, with Chris Serrano and Pape Sylla, preprint, 2020.
- Introspection learning, with Chris Serrano, AAAI Spring Symposium on Verification of Neural Networks (VNN'19), 2019.
Mathematical Logic and Topos Theory
- Lawvere-Tierney sheaves in algebraic set theory, with Steve Awodey, Nicola Gambino and Peter LeFanu Lumsdaine, Journal of Symbolic Logic, 74(3), pp. 862-890, 2009. Preprint on the arXiv.
- Coalgebras in a category of classes, Annals of Pure and Applied Logic, 146(1), pp. 60-71, 2007. Preprint available here.
- Algebraic models of sets and classes in categories of ideals, with Steve Awodey and Henrik Forssell, preprint, 2006.
- Predicative algebraic set theory, with Steve Awodey, Theory and Applications of Categories, 15, pp. 1-39, 2005.
- Predicative categories of classes, M.Sc. Thesis in Logic, Carnegie Mellon University, 2004.
About
Here you can find my contact and biographical information.Contact information
maw@mawarren.net
Previous academic positions
- Member, School of Mathematics, Institute for Advanced Study, Princeton, USA, 2011 - 2013.
- Postdoctoral fellow, Department of Mathematics and Statistics, Dalhousie University, Halifax, Canada, 2010 - 2011.
- Postdoctoral fellow, Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada, 2008 - 2010.
Education
- Ph.D. in Logic, Computation and Methodology, Carnegie Mellon University, Pittsburgh, USA, 2008.
- M.Sc. in Mathematical Sciences, Carnegie Mellon University, 2006.
- M.Sc. in Logic and Computation, Carnegie Mellon University, 2004.
- M.A. (honours, first) in Philosophy, University of St. Andrews, Scotland, UK, 2002.
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