I am an algebraic geometer with broader interests in algebra, geometry, representation theory, and number theory. This means that I study algebraic varieties—spaces of solutions of algebraic equations. Instead of studying one algebraic variety in isolation, I study the collection of all related algebraic varieties at once, using the remarkable feature that such a collection itself forms an algebraic variety (often called a “moduli space”).
I have worked on moduli spaces of algebraic curves, branched covers of curves, surfaces, vector bundles, and so on. For my papers and preprints, see my research page.
Just after graduate school, I wrote a rough non-technical explanation of my doctoral research, which might interest or amuse you.
Upcoming and current activities
- May 6 to 10, 2019: Recent progress in moduli theory, MSRI, Berkeley, CA.
- June 24 to 28, 2019: Workshop on Triangulated Categories, Sydney.
This summer (southern hemisphere), I am co-running a reading course on “Elliptic curves and modular forms” by Neil Koblitz with James Tener. Here are the notes of some of the other advanced classes I have taught.
For other courses taught in the past, see my teaching page.
I wrote a mystery hunt style puzzle.