# Research and publications

My research is in algebraic topology, artificial intelligence, and quantum physics.

I am involved with The Initiative for Theoretical Sciences at the CUNY Graduate Center. Check out the ITS calendar to see what's going on.

Topology Book: Topology: A Categorical Approach is a graduate-level textbook that presents basic topology from the perspective of category theory.

## Selected papers:

- The structure of meaning in language, with T.-D. Bradley and J.-L. Gastaldi, Notices of the American Mathematical Society, Feb 2024.
- An enriched category theory of language: from syntax to semantics, with T.-D. Bradley and Y. Vlassopoulos, La Matematica 2022.
- Tensor networks for probabilistic sequence modeling, with J. Miller and G. Rabusseau, Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:3079-3087, 2021. Code at https://github.com/jemisjoky/umps_code
- Modeling Sequences with quantum states: a look under the hood, with T.-D. Bradley and E. M. Stoudenmire, Machine Learning: Science and Technology, 2020. Code at https://github.com/emstoudenmire/parity.
- Probabilistic modeling with matrix product states, with J. Stokes, Entropy 2019, 21, 1236. Code at https://github.com/TunnelTechnologies/dmrg-exact.
- Language as a matrix product state with V. Pestun and Y. Vlassopolous, eprint arXiv:1711.01416, 2017.
- Homotopy probability theory on a Riemannian manifold and the Euler equation with G.-C. Drummond-Cole, New York Journal of Mathematics, Volume 23 (2017) 1065–1085.
- Algebras over cobar coFrobenius with G.-C. Drummond-Cole and Thomas Tradler, J. Homotopy and Relat. Struc., 2010, Vol 5, No. 1, pp. 15–36.
- Smoothness theorem for differential BV algebras, J. Topology (2008), Vol 1, Issue 3, 693–702.
- Thermodynamic interpretation of the quantum error correcting criterion with V. Korepin, J. Quantum Information Processing (2002) 1: 225–242.

## PhD Students

Current students

- Samantha Jarvis

Past students

- Tyler Bryson 2023. Thesis:
*An Explicit Construction of Sheaves in Context*→ Prescient Design. - Tai-Danae Bradley
2020. Thesis:
*At the Interface of Algebra and Statistics*→ Postdoc at X - The Moonshot Factory. - Joseph Hirsh
2013. Thesis:
*Derived Deformation Theory*→ NSF Postdoc at MIT. - Gabriel
Drummond-Cole 2010. Thesis:
*Homotopy Batalin-Vilkovisky algebras, trivializing circle actions, and moduli space*→ NSF Postdoc at Northwestern.