Research
My research interests are category theory and algebraic topology.
There is a full list of my papers, preprints, and talks in my CV.
Selected Talks
2026 International Category Conference: A Categorical Framework for Coherence Theorems. Accepted: to be given.
2026 Joint Mathematics Meetings: AMS Special Session on New Voices in Homotopy Theory, A categorical framework for coherence theorems.
2025 Young Homotopy-Theorist Meeting: A categorical framework for coherence theorems. Abstract, Video
2025 Joint Mathematics Meetings: AMS Special Session on Applied Category Theory, Applications of Category Theory to Advanced Air Mobility Architecture. Abstract
2023 Applied Category Theory Conference: Monoidal structures on generalized polynomial categories.
2023 Joint Mathematics Meetings: AMS Special Session on Applied Category Theory (a Mathematics Research Communities Session), Monoidal structures on generalized polynomial categories. Abstract
2022 AGI Conference: Technical Keynote, Polynomial Functors: Natural Formal Models of Interaction. Video
Selected Works
D. DeMark, M. A. Hill, Y. Kamel, N. Niu, K. Stoeckl, D. Van Niel, & G. Yan. “Maximal compatibility of disklike G-transfer systems.” Apr. 2026. arXiv:2604.00335
M. Mahlum, S. Jarvis, N. Niu, A. Aguinaldo, A. Hicks, & I. Levitt. “Formal Structures in Systems Ontology towards Air Traffic Management Architectures.” National Aeronautics and Space Administration, Nov. 2025. NASA/TM-20250010771
N. Niu & D. I. Spivak. Polynomial Functors: A Mathematical Theory of Interaction. Cambridge University Press, Oct. 2025. doi:10.1017/9781009576734
J. Dorta, S. Jarvis, & N. Niu. “Monoidal Structures on Generalized Polynomial Categories.” Proceedings of the Sixth International Conference on Applied Category Theory, Electronic Proceedings in Theoretical Computer Science, vol. 397, pp. 84–97, Dec. 2023. doi:10.4204/EPTCS.397.6
N. Niu & D. I. Spivak. Collectives: Compositional protocols for contributions and returns. Dec. 2021. arXiv:2112.11518
Selected Service
2026 Joint Mathematics Meetings: AMS Special Session on Applied Category Theory, Co-Organizer.
2025 Joint Mathematics Meetings: AMS Special Session on Applied Category Theory, Co-Organizer.