I currently have no graduate advisees and one postdoctoral advisee, Matt Mastroeni.
I study computational commutative algebra and algebraic geometry. I use a lot of Macaulay2 in my research, so a willingness to write code is useful. Students who end up working with me will eventually need to become familiar with the major ideas in texts like "Commutative Algebra with a View Toward Algebraic Geometry" and "The Geometry of Syzygies" by Eisenbud, or "Graded Syzygies" by Peeva. These are all wonderful textbooks that could be used as reading course material.
If you are interested in working with me, I encourage you to come and talk to me early in your graduate career. Generally speaking I want students to have taken at least one class with me before I become their PhD advisor, though I'm happy to help you find the right PhD advisor even if it's not me. The following courses are most useful for my area of research: Math 504/505 Abstract Algebra I and II, Math 619 Commutative Algebra, Math 511 Complex Analysis, Math 624 Manifolds, Math 502 Topology, and Math 506 Algebraic Topology. (Also relevant: Math 510 Linear Algebra, Math 567 Graph Theory, Math 568 Enumerative Combinatorics, Math 617 Category Theory, Math 618 Representation Theory)
|Joshua Rice (PhD)
|Generic Lines in Projective Space and the Koszul Property, Nagoya Math. J. 2023.
|Tenure-track assistant professor at the University of the Virgin Islands
|Zachary Greif (MS)
|Green-Lazarsfeld Index of Toric Edge Ideals of Bipartite Graphs, J. Alg, 2020.
|Undergraduate Research Advisee
|Andrew Osborne and Cole Willis
|Depth and Singular Varieties of Exterior Edge Ideals, submitted.
|Graduate student at University of Minnesota (Willis)
G-quadratic, LG-quadratic, and Koszul
quotients of exterior algebras, Comm. in Alg.. 2022
|Graduate student at University of Utah
Green-Lazarsfeld condition for toric edge
ideals of bipartite graphs, J. Alg., 2020
|Graduate student at Iowa State
Asymptotically good homological error
correcting codes, JACODESMATH, 2019
|Graduate student at Drexel University