David Green
I am at the Department of Mathematics at North Carolina State University. I'm broadly interested in quantum algebra and category theory. Right now, I'm thinking about reconstruction theorems for monoidal 2-categories, and the structure and obstruction theories for Hopf monoidal categories.
Here is my CV (Last updated March 2026).
These are my articles on the arXiv.
My ORCID profile.
Current Projects
Hopf Multifusion Categories I: Reconstruction
I am currently revising my extension of the Tannakian formalism to fusion 2-categories.
Hopf Multifusion Categories II: Classification
A classification of all multifusion Hopf monoidal categories. Joint with Brett Hungar and Sean Sanford.
Research & Publications
Published Works
- David Green, Yoyo Jiang, and Sean Sanford. "Braidings for Non-Split Tambara-Yamagami Categories over the Reals." Transformation Groups (2026).
- Kyle Kawagoe, Corey Jones, Sean Sanford, David Green, and David Penneys. "Levin-Wen is a Gauge Theory: Entanglement from Topology". Communications in Mathematical Physics 405.11 (Oct. 2024).
- David Green, Peter Huston, Kyle Kawagoe, David Penneys, Anup Poudel, and Sean Sanford. "Enriched string-net models and their excitations". Quantum 8 (Mar. 2024).
- Jessica M. Christian, David Green, Peter Huston, and David Penneys. "A lattice model for condensation in Levin-Wen systems". Journal of High Energy Physics (2023).
Preprints
- David Green. "Tannaka-Krein reconstruction for fusion 2-categories." (2023) arXiv:2309.05591.
Upcoming Travel
- July 7-10, 2026: MMRT 2026
- July 13-18, 2026: CT 2026
- [Tenative] August 17-21, 2026: Future Directions in Tensor Categories
- [Tenative] August 21-24, 2026: Tensor categories in representation theory & vice versa
Other Activities
- During Summer 2020 I did a reading course with Daniel Packer and Amogh Parab under Niles Johnson and produced this document.
- Ohio State Taekwondo Club: President (2022-2023) and Senior Instructor / Primary competition coach (Jun 2022 - May 2025).
- I am interested in starting a sport Taekwondo club at NCSU. If you share this interest, email me.