Reading courses

In my view, a reading course is one of the best ways to get a feel for what it's like to independent work in advanced mathematics. Even better, you get to learn some really cool stuff while doing so, often things which aren't covered by the standard curriculum. (They're also a great way to get to know individual faculty members and to get a sense for how you would perform in doing independent learning in graduate school.) 

If you have something you're interested in reading about but don't know who to talk to about it, feel free to write to me!

While I was at Columbia, I directed 8 reading courses with 13 different students in a wide variety of areas (see my CV for a full list), and I will direct 2 reading courses this year at UVM.

Theses

2022-2023: Arjun Kudinoor wrote on the early interaction between mathematicians and physicists in the study of gauge theory, in particular instanton gauge theory, culminating in a sketch of the proof of the Atiyah-Hitchin-Singer theorem. His thesis, "Geometry and gauge-theoretic physics: an instanton connection" is available here. 

Arjun is now studying mathematics at Part III in Cambridge, and will start his PhD in physics at MIT in Fall 2024.

Undergraduate research

In Summer 2022 I worked with Aiden Sagerman on joint work in algebra and topology, focused on cancellation problems for certain products. See the Research tab above for a more extensive description, and a link to our paper. 

Research in mathematics has a notoriously high barrier to entry, and tends to be accessible primarily to Junior and Senior-level students who have taken extensive coursework. Still, I do have some projects which should be accessible for students, and many departments run REUs which include some training in the relevant background material.

If you are interested in doing research with me (or exploring research in general), please feel free to reach out; whether or not I have the time to supervise a project, I will try to give useful advice on where to look.

A particularly fearsome mathematician begins mentoring an interested student. Art by Ryan Armand.