Mathematics

I’m a mathematician, philosopher, writer... hopeful inventor?

My interests are very broad, crossing the boundaries of STEM and the humanities, academia and industry. Currently I serve as an Assistant Professor in the Center for Applied Mathematics at UVA.

I studied under Raphaёl Rouquier for my PhD at UCLA, finishing in 2023. In my dissertation in higher quantum algebra I developed a tensor 2-product for 2-representations of Lie algebras. I am hoping that this operation will yield a totally new construction of Khovanov homology, and perhaps one day lead to an interesting 4D TQFT. I also have math research projects about quantum group asymptotics and Calogero Moser cells.

Since 2023 my attention has been focused primarily on my teaching and the development of a major pedagogy initiative called xTensiv. This project aims to replace math textbooks with a “learnable library,” a web-scale database of text and problems equipped with learn-order data, allowing computer generation and graphical navigation of all possible and feasible learning pathways through the library. The purpose is to provide for efficient goal-directed learning and effective exploratory learning.

I am nearly finished with my first book, entitled “G. W. Leibniz, The Philosophy of Situation. ‘Geometric Characteristic’ and other essays on anaylsis situs.” This book will provide translation of, and commentary upon, Leibniz’s analysis situs project. (Publication anticipated in 2026.)

I am slowly working on publishing additional writing in philosophy from my years in Oxford, and I have a series of essays planned out about the nature of mathematics.