David Green

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.

Tannakian Formalism for Monoidal 2-categories
A Tannakian formalism that extends beyond semisimple 2-categories. Joint with Nick Gurski and David Yetter.

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 24-27, 2026: Tensor categories in representation theory & vice versa
  • November 7-8, 2026: AMS Fall 2026 Western Sectional Meeting
Other Activities and Writings
  • Ohio State Taekwondo Club: President (2022-2023) and Senior Instructor / Primary competition coach (Jun 2022 - May 2025).
  • I will be coaching the NC State Taekwondo Club starting Fall 2026
  • During Summer 2020 I did a reading course with Daniel Packer and Amogh Parab under Niles Johnson and produced this document.
  • © David Green.
  • Credits: HTML5 UP