Tai-Danae Bradley

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

I am currently a research mathematician at Sandbox AQ and a visiting professor of mathematics at The Master's University where I help run the Math3ma Institute. I finished my PhD in mathematics in spring 2020 at the CUNY Graduate Center under the supervision of John Terilla and spent some time as a postdoctoral researcher at X, the Moonshot Factory (Google X). My research interests lie in the intersection of quantum physics, machine intelligence, and category theory.

Below is a list of my research, publications, and more.

**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. Here is a 10-minute trailer video:

**Topology: A Categorical Approach **[online version]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

**The Structure of Meaning in Language: Parallel Narratives in Linear Algebra and Category Theory **[PDF]with Juan Luis Gastaldi and John Terilla,

**An Enriched Category Theory of Language: From Syntax to Semantics **[video]with John Terilla and Yiannis Vlassopoulos

**Entropy as a Topological Operad Derivation **[video]*Entropy 2021, 23(9), 1195*. doi.org/10.3390/e23091195

**Probabilistic Graphical Models and Tensor Networks: A Hybrid Framework**with Jacob Miller and Geoffrey Roeder. arXiv pre-print: 2106.15666

**Language Modeling with Reduced Densities **[video]with Yiannis Vlassopoulos,

Modeling Sequences with Quantum States: A Look Under the Hood

doi.org/10.1088/2632-2153/ab8731, code available at https://github.com/emstoudenmire/parity

**Translating and Evolving: Towards a Model of Language Change in DisCoCat**with Martha Lewis, Jade Master and Brad Theilman,

**On the Distribution 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

**A New Perspective of Entropy **[video]A companion article to "Entropy as a Topological Operad Derivation" written for the ambitious lay person.

**What is Applied Category Theory?**A short expository booklet inspired by the 2018 Applied Category Theory conference

e-booklet, arXiv: 1

**An Invitation to Category Theory**A non-technical introduction to category theory

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) ****

**Linear Algebra for Machine Learning**A friendly, non-technical intro to basic ideas in linear algebra and some ways they appear in machine learning

**PBS Infinite Series (Season 2)**A series of short videos produced by PBS Digital Studios about the wonderful world of mathematics

An article from **The Brilliant** (April 2023)

A video interview with Miles Stoudenmire at the **Flatiron Institute** (August 2022)

A podcast interview on Timothy Nguyen's **The Cartesian Cafe **(July 2022)

A podcast interview on Sean Carroll's **Mindscape** (November 2021)

An interview article in *Math Horizons**,* volume 29, issue 2 (November 2021)

A video interview on Grant Sanderson's **3Blue1Brown Podcast** (September 2021)

A video interview on **MΣΣT a Mathematician** (February 2021)

A podcast interview on **My Favorite Theorem** (January 2021)

A podcast interview on** The Local Maximum** (November 2020)

An article from the **CUNY Graduate Center** (November 2020)