I am currently a postdoc at X, the Moonshot Factory (formerly Google X). I finished my PhD in mathematics in spring 2020 at the CUNY Graduate Center under the supervision of John Terilla. My research interests lie in the intersection of quantum physics, machine intelligence, and category theory. Below is a list of my research and publications.

PhD Thesis

At the Interface of Algebra and Statistics My thesis uses basic tools from quantum physics to investigate mathematical structure that is both algebraic and statistical. arXiv: 2004.05631, introductory video

Books

Topology: A Categorical Approach A graduate-level textbook that presents basic topology from the perspective of category theory with Tyler Bryson and John Terilla, published by MIT Press (release date: August 18, 2020) Here is the book's website.

What is Applied Category Theory? A short expository booklet inspired by the 2018 Applied Category Theory conference ebook, arXiv: 1809.05923

Papers

Language Modeling with Reduced Densities An assignment of reduced densities to words in a natural language, which is shown to be a functor between categories enriched over probabilities with Yiannis Vlassopoulos, arXiv preprint: 2007.03834 Modeling Sequences with Quantum States: A Look Under the Hood An algorithm for training an MPS generative model inspired by the density matrix renormalization group with Miles Stoudenmire and John Terilla Machine Learning: Science and Technology, 2020. arXiv: 1910.07425, code available at https://github.com/emstoudenmire/parity

Translating and Evolving: Towards a Model of Language Change in DisCoCat A categorical approach to representing translations within the DisCoCat language model with Martha Lewis, Jade Master and Brad Theilman Electronic Proceedings in Theoretical Computer Science 283 (2018) pp. 50-61. arXiv: 1811.11041

On the Distribution of the Greatest Common Divisor of Gaussian Integers Asymptotics for the average norm of the greatest common divisor of Gaussian integers with Yin Choi Cheng and Yan Fei Luo Involve, A Journal of Mathematics, vol. 9, issue 1 (2016), pp. 27-40. arXiv: 1502.02148

Exposition

An Invitation to Category Theory A non-technical introduction to category theory Chalkdust Magazine, Issue 08 (2018) pp. 22-25. online version here

Cognition, Convexity, and Category Theory A short summary of the paper "Interacting conceptual spaces" by Coecke, et. al. n-Category Café blog post (2018)

Entropy as an Operad Derivation A proof that Shannon entropy defines a derivation on the operad of topological simplices personal notes(2017)