The lost art of diagramming sentences
Graham J. Leuschke
I am a Professor of Mathematics at Syracuse University. leuschke.org is where I keep web versions of my professional work: (p)reprints of papers, my book with Roger Wiegand, Cohen–Macaulay Representations, slides from talks, information about my teaching, and other projects.
For a quick overview of what else I do, you may be interested in my curriculum vitae. Please feel free to email me for more information, or just to say hi.
Research
What I work on
The recurring theme is that modules — especially maximal Cohen–Macaulay ones — carry precise information about the singularities of the rings over which they live.
Cohen–Macaulay representation theory
Finite, countable, and bounded Cohen–Macaulay type; Brauer–Thrall theory; direct-sum decompositions over local rings.
Noncommutative resolutions
Noncommutative crepant resolutions of determinantal varieties, endomorphism rings of finite global dimension, and derived categories.
Matrix factorizations
Hypersurface singularities, branched covers, Knörrer periodicity, and factorizations with more than two factors.
Also, less tidily: the F-signature and strong F-regularity, the growth of Betti sequences, rings with nontrivial semidualizing modules, and the Auslander–Reiten conjecture. Research overview, papers, and talks →
People
Mentoring
Eight doctoral students have completed dissertations with me; I have supervised three postdoctoral scholars and served on more than twenty dissertation committees across mathematics, physics, engineering, and mathematics education.
Doctoral students
Bhargavi Parthasarathy (2026), Ben Kaufman (2026, co-advised with Dan Zacharia), Kaiyue He (2025), Richard Bartels (2024), Tim Tribone (2022), Özgür Esentepe (2019), Robert Roy (2018), Joshua Stangle (2017).
Postdoctoral scholars
Rebecca R.G. (2016–2018), Denise Rangel Tracy (2014–2016), Andrew Crabbe (2008–2010).
If you are a prospective graduate student interested in commutative algebra or representation theory, please get in touch. Students, postdocs, and advising →
Service
A website, two journals, and a lot of conferences
Commutative algebra is a community of manageable size, which means the things it runs on tend to get built by the people who use them.
commalg.org
Co-founder, designer, and co-webmaster from 2001 to 2021, with Moira McDermott and Keri Sather-Wagstaff — conference announcements, news, and links for commutative algebraists.
Editorial boards
Associate Editor for the Journal of Commutative Algebra (2007–2016) and Communications in Algebra (2012–2023).
AMS service
Member at Large and then Chair of the AMS Committee on Meetings and Conferences, 2013–2016.
Selected links
Two books and a long survey
Cohen–Macaulay Representations
The book with Roger Wiegand: a survey of the representation theory of maximal Cohen–Macaulay modules over local rings, from the McKay correspondence through to Brauer–Thrall.
Twenty-Four Hours of Local Cohomology
A one-week graduate course, written up with Iyengar, Leykin, Miller, Miller, Singh, and Walther. My four lectures are on the talks page.
Noncommutative crepant resolutions
An expository tour, “scenes from categorical geometry,” written for algebraists arriving from the commutative side.