Matthew McMillan
mcmillan@virginia.edu

Mathematics

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Philosophy  ·  Psychology  ·  Pedagogy

About

Matthew McMillan in Iceland

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, G. W. Leibniz, The Philosophy of Situation: ‘Geometric Characteristic’ and Other Essays on Analysis Situs. This book provides translation of, and commentary upon, Leibniz’s analysis situs project.

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.

Bio Timeline

2023–
Assistant Professor, General Faculty at UVA.

2023
UCLA PhD. Committee: Raphaël Rouquier, Paul Balmer, Burt Totaro, Sergei Gukov.
2022–23
Visiting graduate student at UVA.
2021
Advanced to Candidacy (ABD) at UCLA. Found abelian tensor 2-product.
2019
August: Started translating Leibniz on the analysis situs (with David Jekel).
July: Park City / IAS summer school: Quantum Field Theory and Manifold Invariants.
February: Began study under Raphaël Rouquier.
January: ESI Vienna workshop: Categorification in Quantum Topology.
2018
Princeton summer school: Low-dim Topology and Symplectic Geometry.
2017
Began PhD at UCLA supported by an NDSEG fellowship; began study of Russian.

2017
MPhil (‘BPhil’) degree from Oxford philosophy; ‘Vantage’ certificate in German.
2016
Began study of Latin and work on Leibniz.
2015
MASt degree (‘Part III’) from Cambridge in mathematics.
2014
Began graduate study in the UK supported by a Marshall Scholarship.

2014
BS degree, Mathematics and Physics, from Wheaton College in Illinois.
2013
Summer: Symplectic geometry at UC Berkeley under Dan Cristofaro-Gardiner.
Spring: Budapest Semesters in Mathematics.
2012
Summer: Fusion energy research at PPPL under Samuel Lazerson.
2010–12
Research on the Wheaton Impulsive Reconnection Experiment.