## Research and publications

My work is in algebraic topology, quantum physics, and machine learning.

**Topology: A Categorical Approach** is a graduate-level textbook that presents basic topology from the perspective of category theory. Coauthored with Tai-Danae Bradly and Tyler Bryson and published by MIT Press. It will be released on August 18, 2020.

Selected papers:

- Language Modeling with Tensor Networks, with J. Miller and G. Rabusseau, eprint arXiv:2003.01039, 2020.
- 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.
- Quantizing Deformation Theory in Deformation Spaces, Vieweg Teubner Verlag, 2010.
- Algebras over Cobar CoFrobenius with Gabriel 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 Korepin, V., J. Quantum Information Processing (2002) 1: 225-242.

## PhD Students

Current students

- Tai-Danae Bradley
- Tyler Bryson

Past students

- Joseph Hirsh
PhD May 2013. Thesis:
*Derived Deformation Theory*. NSF Postdoc at MIT. - Gabriel
Drummond-Cole PhD May, 2010. Thesis:
*Homotopy Batalin-Vilkovisky algebras, trivializing circle actions, and moduli space.*NSF Postdoc at Northwestern.