John Nolan

Portrait of me.

I am a PhD student in the Math Department at UC Berkeley. My current research focuses on algebraic geometry and its relationship with topological quantum field theory.

My advisor is Constantin Teleman.

You can reach me at: firstname UNDERSCORE lastname AT berkeley DOT edu.

Current and Recent Projects

  1. I am currently developing an approach to toric stacks based on symmetric monoidal categories. This gives a new perspective on classical results such as the Cox construction and can be used to establish a workable derived analogue of toric geometry. Paper coming soon!
  2. (arXiv) With Daigo Ito, I studied a family of "extended convolution" tensor products on derived categories of coherent sheaves on toric varieties. These can be used to answer some natural questions in homological mirror symmetry and also give some hitherto-unconsidered examples of monoidal structures on derived categories of projective spaces.

Old Publications

(I publish as John S. Nolan.)

  1. Amplitudes in persistence theory. With Barbara Giunti, Nina Otter, and Lukas Waas. In: Journal of Pure and Applied Algebra.
  2. Symmetric Monoidal Categories with Attributes. With Spencer Breiner. In: Proceedings of the 3rd Annual International Applied Category Theory Conference 2020.
  3. Compositional Models for Power Systems. With Blake S. Pollard, Spencer Breiner, Dhananjay Anand, and Eswaran Subrahmanian. In: Proceedings of the 2nd Annual International Applied Category Theory Conference 2019.
  4. A Generalization of Gleason's Frame Function for Quantum Measurement. With John J. Benedetto and Paul J. Koprowski.

Notes

In recent years, I have been live-TeXing various seminars and conferences. Here are links to my notes from a few of them:

  1. Berkeley Geometric Representation Theory seminar, organized by David Nadler and students (notes from Fall 2023-present)
  2. Berkeley Low-Dimensional Gauge Theory seminar, organized by Constantin Teleman (Fall 2025).
  3. Berkeley Commutative Algebra and Algebraic Geometry seminar, organized by David Eisenbud, Hannah Larson, and students (notes from Fall 2024-Spring 2025)
  4. Berkeley Student Stable Homotopy Theory seminar, organized by Joe Hlavinka and Kabir Kapoor (Spring 2025)
  5. Berkeley Student Arithmetic Geometry seminar, organized by Martin Olsson (notes from Fall 2024)
  6. BIRS-CMO Conference on Equivariant Topological Quantum Field Theory (Fall 2025)
  7. Simons Collaboration on Global Categorical Symmetries summer school (Summer 2024)
  8. SLMath summer school on Derived Algebraic Geometry, taught by Ben Antieau and Dima Arinkin (Summer 2023)