John Terilla - Mathematician
Topology, AI, and Quantum
My work is in algebraic topology, artificial intelligence, and quantum physics. I currently serve as the Executive Officer of the PhD Program in Mathematics at the CUNY Graduate Center and I’m involved with the Initiative for Theoretical Sciences.
Selected Papers
- From language models over tokens to language models over characters — with T. Vieira et al.
- The foundations of tokenization: statistical and computational concerns — with J.-L. Gastaldi et al.
- The structure of meaning in language — with T.-D. Bradley & J.-L. Gastaldi.
- An enriched category theory of language: from syntax to semantics — with T.-D. Bradley & Y. Vlassopoulos.
- Modeling sequences with quantum states: a look under the hood — with T.-D. Bradley & E. M. Stoudenmire.
- Probabilistic modeling with matrix product states — with J. Stokes.
- Language as a matrix product state — with V. Pestun & Y. Vlassopoulos.
- Homotopy probability theory on a Riemannian manifold and the Euler equation — with G.-C. Drummond-Cole.
- Algebras over cobar coFrobenius — with G.-C. Drummond-Cole & T. Tradler.
- Quantum backgrounds and QFT — with T. Tradler & J.-S. Park.
- Smoothness theorem for differential BV algebras —
PhD Students
- Samantha Jarvis (2025). Thesis: A Novel Closed Monoidal Structure on the Nucleus of a Profunctor.
- Tyler Bryson (2023). Thesis: An Explicit Construction of Sheaves in Context.
- Tai-Danae Bradley (2020). Thesis: At the Interface of Algebra and Statistics.
- Joseph Hirsh (2013). Thesis: Derived Noncommutative Deformation Theory.
- Gabriel Drummond-Cole (2010). Thesis: Homotopy Batalin–Vilkovisky algebras, trivializing circle actions, and moduli space.
Topology — A Categorical Approach
A graduate-level textbook that presents basic topology from the perspective of category theory. Chapter PDFs are available open access.