I currently have one graduate advisee (Matthew Dorang).

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)

Previous Advisees

Postdoctoral Advisee | Years | Publications | First Position |
---|---|---|---|

Matthew Mastroeni | 2021-2024 | Chow Rings of Matroids are Koszul, Depth and singular varieties of exterior edge ideals, to appear in Rocky Mountain Journal of Mathematics. | Tenure-track assistant professor SUNY Polytechnic |

Graduate Advisee | Years | Publications | Thesis | First Position |
---|---|---|---|---|

Joshua Rice (PhD) | 2018-2023 | Generic Lines in Projective Space and the Koszul Property, Nagoya Math. J. 2023. Depth and singular varieties of exterior edge ideals, to appear in Rocky Mountain Journal of Mathematics. | Tenure-track assistant professor at the University of the Virgin Islands | |

Zachary Greif (MS) | 2018-2022 | Green-Lazarsfeld Index of Toric Edge Ideals of Bipartite Graphs, J. Alg, 2020. |

Undergraduate Research Advisee | Years | Publications | First Position |
---|---|---|---|

Andrew Osborne and Cole Willis | 2022 | Depth and Singular Varieties of Exterior Edge Ideals, submitted. | Graduate student at University of Minnesota (Willis) |

Zach Mere | 2019-2021 | G-quadratic, LG-quadratic, and Koszul quotients of exterior algebras, Comm. in Alg.. 2022 | Graduate student at University of Utah |

Zach Greif | 2017-2018 | Green-Lazarsfeld condition for toric edge ideals of bipartite graphs, J. Alg., 2020 | Graduate student at Iowa State |

Heather Newman | 2015-2017 | Asymptotically good homological error correcting codes, JACODESMATH, 2019 | Graduate student at Drexel University |