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 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

• Nelson Niu and David I. Spivak. Polynomial Functors: A Mathematical Theory of Interaction. Cambridge University Press, Oct. 2025. doi:10.1017/9781009576734

• Joseph Dorta, Samantha Jarvis, and Nelson 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

• Nelson Niu and David 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.