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 Foundations of Tokenization: Statistical and Computational Concerns, with J.-L. Gastaldi, et al. July 2024.
• 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.
• 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.
• Quantum backgrounds and QFT with T. Tradler and J.-S. Park, Inter. Math. Res. Notices, Issue 5, 2009.
• Smoothness theorem for differential BV algebras, J. Topology (2008), Vol 1, Issue 3, 693–702.

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.