Teaching Interests
At UVA I have taught across the undergraduate mathematics curriculum in ‘concrete’ math classes: Calculus I, II, and III, Probability, Applied Linear Algebra, and Differential Equations. Recently my focus has been on Probability.
I am especially interested in innovative courseware management, and in making my material digitally accessible (screen-reader-friendly) using MathML in my course websites.
I am currently developing a new course, Mathematics of Machine Learning, in connection with the proposed Minor in AI Development intended for engineering majors. The full list of courses I have taught is here.
Fall 2026: Probability
This semester I am teaching three sections of Probability. The course now runs on a hybrid mastery grading scheme: mastery grading (binary, multiple attempts) for core learning targets that are dependencies of later material; traditional grading (fractional, midterms and final) for terminal learning targets.
Research Interests
My mathematical research is in higher representation theory and quantum algebra. I constructed a tensor 2-product for 2-representations of sl(2), and I hope this operation will yield a new construction of Khovanov homology.
What are “higher” representations? Here is a short expository article for a general math audience by my PhD advisor, Raphaël Rouquier, whose early work was foundational in this area.
I also work on the history and philosophy of mathematics, especially Leibniz and Wittgenstein, and on mathematics education. The general theme of my philosophical interest is meaning in compositional arts including mathematics, music, and code. I am also interested in philosophical aspects of geometry, physics (particularly spacetime and quantum physics), and science more broadly.
Papers and work in progress are here.
xTensiv
xTensiv is a pedagogy initiative that aims to replace math textbooks with a “learnable library”: a web-scale database of texts and problems provided with metadata and relational data, so that learning pathways toward any chosen learning target can be generated by computer and navigated on a map. The purpose is to provide for efficient goal-directed learning and productive exploration in a subject that is traditionally hard to learn outside of formal instruction following linear paths.
The library currently houses over 800 pages of learning material, which you can browse here.
Leibniz
I am editing G. W. Leibniz: The Philosophy of Situation. This is a collection of Leibniz’s writings on his analysis situs, most of which have no English edition. David Jekel is my co-translator. The book is set to be published by Oxford University Press in the series New Texts in the History of Philosophy, hopefully in 2027.
Draft translations, official transcriptions, and processed manuscripts are available on the Leibniz page.
This project got a little press at UVA in 2024.