Tai-Danae Bradley

tai [dot] danae [at] math3ma [dot] com

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


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 2020
free online at topology.mitpress.mit.edu

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


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 (2020). 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


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)