I am a research mathematician at Sandbox AQ, which originated within Alphabet Inc., and was previously a postdoc at X, the Moonshot Factory. I am also a visiting research 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. 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. page 
# 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:
YOUTUBE wiadG3ywJIs At the Interface of Algebra and Statistics
> This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. > > The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals recover classical marginal probabilities. In general, these reduced densities will have rank higher than one, and their eigenvalues and eigenvectors will contain extra information that encodes subsystem interactions governed by statistics. We decode this information, and show it is akin to conditional probability, and then investigate the extent to which the eigenvectors capture "concepts" inherent in the original joint distribution. The theory is then illustrated with an experiment that exploits these ideas. Turning to a more theoretical application, we also discuss a preliminary framework for modeling entailment and concept hierarchy in natural language, namely, by representing expressions in the language as densities. > > Finally, initial inspiration for this thesis comes from formal concept analysis, which finds many striking parallels with the linear algebra. The parallels are not coincidental, and a common blueprint is found in category theory. We close with an exposition on free (co)completions and how the free-forgetful adjunctions in which they arise strongly suggest that in certain categorical contexts, the "fixed points" of a morphism with its adjoint encode interesting information.