Mathematician

John Terilla

Algebraic topology · artificial intelligence · 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.

Abstract painting by David Scher: a pale field of scattered marks, faint pencil lines, letters, and muted fragments of blue, ochre, and grey.
Banner artwork by David Scher.

Selected papers

  1. A calculus of types in Isbell nuclei with J.-L. Gastaldi, S. Jarvis & T. Seiller preprint 2026
  2. Projective metric geometry of tropical nuclei: gap matrices, event loci, and order chambers with J.-L. Gastaldi, S. Jarvis & T. Seiller preprint 2026
  3. The foundations of tokenization: statistical and computational concerns with J.-L. Gastaldi et al. ICLR 2025
  4. The structure of meaning in language with T.-D. Bradley & J.-L. Gastaldi Notices of the AMS, Feb 2024
  5. An enriched category theory of language: from syntax to semantics with T.-D. Bradley & Y. Vlassopoulos La Matematica, 2022
  6. Probabilistic modeling with matrix product states with J. Stokes Entropy, 2019
  7. Language as a matrix product state with V. Pestun & Y. Vlassopoulos unpublished, 2017
  8. Homotopy probability theory on a Riemannian manifold and the Euler equation with G.-C. Drummond-Cole New York J. Math., 2017
  9. Algebras over cobar coFrobenius with G.-C. Drummond-Cole & T. Tradler J. Homotopy & Relat. Struct., 2010
  10. Quantum backgrounds and QFT with T. Tradler & J.-S. Park IMRN, 2009
  11. Smoothness theorem for differential BV algebras J. Topology, 2008

Book

Cover: Topology — A Categorical Approach

Topology — A Categorical Approach

A graduate-level textbook that presents basic topology from the perspective of category theory. Chapter PDFs are available open access.

Book page

PhD students