theory
Research
Applied category theory, sheaf theory, and formal methods to study a wide range of systems.
My work is in applied category theory and sheaf theory. Lately it runs in three directions: turning informal specifications into machine-checked safety guarantees for real-world systems using temporal type theory; pinning down where complex systems fail to compose and principled ways to handle these obstructions; and finding interpretable structure in high-dimensional, time-varying data.
Publications
- Sheaf Theory through Examples MIT Press Read open-access
- A Parameterized Algorithm for Testing whether the Limit of a Diagram is Empty arXiv:2605.24240
- Sheaf Theory through Exercises In progress · with Benjamin Bumpus
- Algorithmic and Extremal Obstructions Through the Language of Cohomology arXiv:2407.03488
- How Nice is this Functor? Two Squares and Some Homology go a Long Way Applied Category Theory 2024 / MFPS · Oxford Talk video
- Compositional Algorithms on Compositional Data: Deciding Sheaves on Presheaves arXiv:2302.05575
- Towards a Classification of Continuity and On the Emergence of Generality PhD dissertation · DePaul University AbstractTable of contents
Selected talks
- How to Use Sheaf Toposes for Structured Temporal Data AMS Joint Mathematics Meeting 2025 · Seattle
- A Vast and Calm River: Unique Factorization Lifting Functors and Sheaves UCLA Institute for Pure and Applied Mathematics (IPAM) · Fellows Seminar
- The Ising Model in 2D via Category Theory University of Florida · GATAS Lab
- Sheaf Cohomology for Tracking Emergent Effects Wytham Abbey, Oxford · Emergence & Non-Compositionality in Complex Systems
- Sheaves for Complex System Modeling and Design SIG Mines Paris Design Theory Workshop
- Some Propaganda for Sheaves: how to think about them, what to use them for, and where to find them NIST Workshop on Compositional Structures in Systems Engineering and Design
Full list on Google Scholar · arXiv
Random / old stuff
- Enriching over Tolerance Spaces MIT · Applied Categories Seminar
- A Philosophical Fantasy Chicago WildSounds · Art, Philosophy & Science of Sound Conference