## Teaching

In Fall 2022, I am teaching Math 152 - Calculus 2 at Queens College and Math 70700 - Topology at the CUNY Graduate Center. I am also involved with The Initiative for Theoretical Sciences at the CUNY Graduate Center and the tutorials and symposia hosted there.

## Research and publications

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

**Topology: A Categorical Approach** is a graduate-level textbook that presents basic topology from the perspective of category theory. Coauthored with Tai-Danae Bradley and Tyler Bryson and published by MIT Press. Reviewed in the AMS Notices Septebmer, 2022: Book review: Topology: A Categorical Approach.

Selected papers:

- 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

- Constantijn van der Poel
- Samantha Jarvis
- Tyler Bryson

Past students

- 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.