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

2027 (upcoming)

• Joint Mathematics Meetings: AMS Special Session on Mathematics of Complex Data Models in Scientific Workflows, Double (the) Categories: Applying Categorical Logic to Applied Categorical Modeling.

2026

• Topos Institute Berkeley Seminar: A loose Yoneda theory for equipments. Video

• Topos Institute Berkeley Seminar: A Categorical Framework for Coherence Theorems. Video

• International Category Conference: A Categorical Framework for Coherence Theorems.

• 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

• 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.

• 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.