Students & Mentoring
Advising is the work
Most of what I know about commutative algebra I learned in the company of other people — my own advisor, my coauthors, and the students and postdocs who have worked with me at Syracuse.
Doctoral students
- Bhargavi Parthasarathy (2026) — Homomorphisms of maximal Cohen-Macaulay modules over the cone of general elliptic curves, Syracuse University.
- Ben Kaufman (2026) — On the extension conjecture for Koszul algebras, Syracuse University. Co-advised with Dan Zacharia.
- Kaiyue He (2025) — Betti numbers for modules over Artinian local rings, Syracuse University.
- Richard Bartels (2024) — Numerical invariants of Cohen-Macaulay local and graded rings, Syracuse University.
- Tim Tribone (2022) — Matrix factorizations with more than two factors, Syracuse University.
- Özgür Esentepe (2019) — Annihilation of cohomology over Gorenstein rings, University of Toronto.
- Robert Roy (2018) — Auslander-Reiten sequences over Gorenstein rings of dimension one, Syracuse University.
- Joshua Stangle (2017) — Representation theory of orders over Cohen-Macaulay rings, Syracuse University.
Dissertations are available through SURFACE, Syracuse University’s research repository.
Postdoctoral scholars
- Rebecca R.G. (2016–2018), PhD University of Michigan — now on the faculty at George Mason University.
- Denise Rangel Tracy (2014–2016), PhD University of Texas at Arlington — now on the faculty at Francis Marion University.
- Andrew Crabbe (2008–2010), PhD University of Nebraska–Lincoln — then an MD from Penn, and now a hematopathologist at the Cleveland Clinic, where the objects of study are more easily classified than MCM modules.
Prospective graduate students
If you are considering doctoral work in commutative algebra or the representation theory of rings, I am glad to hear from you. The projects I supervise usually begin with a concrete class of rings or modules — hypersurfaces, orders, determinantal rings — and grow outward into homological algebra and category theory as the questions demand it.
Applications to the PhD program are handled by the Department of Mathematics, not by individual faculty, so the most useful first step is to apply and mention algebra as an interest. Feel free to email me in the meantime.
Committees and mentoring beyond my own students
I have served on more than twenty doctoral dissertation committees, including as chair for candidates in physics, electrical engineering and computer science, and mathematics education, and have been a PhD preliminary examiner nearly twenty times since 2007. From 2006 to 2014 I was a mentor in Syracuse’s Preparing Future Faculty program.
In 2018 I received the Excellence in Graduate Education Faculty Recognition Award from Syracuse University.