Jack Jeffries | Research

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My research is in Commutative Algebra. More particularly, my interests include invariant theory, positive characteristic techniques, differential operators, local cohomology, generalized multiplicities, symbolic powers, and applications to neuroscience.

Research Statement    Google Scholar page     arXiv page

1. The j-multiplicity of Monomial Ideals,
with Jonathan Montaño,
Mathematical Research Letters, 20 (2013) no. 4, 729–744.
2. Non-simplicial Decompositions of Betti Diagrams of Complete Intersections,
with Courtney Gibbons, Sarah Mayes, Claudiu Raicu, Branden Stone, and Bryan White,
Journal of Commutative Algebra, 7 (2015), no. 2, 189–206.
3. Multiplicities of Classical Varieties,
with Jonathan Montaño and Matteo Varbaro,
Proceedings of the London Mathematical Society, 110 (2015), no. 4, 1033–1055.
4. Separating Invariants and Local Cohomology,
with Emilie Dufresne,
Advances in Mathematics, 270 (2015) 565–581.
5. What Makes a Neural Code Convex?,
with Carina Curto, Elizabeth Gross, Katherine Morrison, Mohamed Omar, Zvi Rosen, Anne Shiu, and Nora Youngs,
SIAM Journal of Applied Algebraic Geometry, 1 (2017), no. 1, 222–238.
6. Appendix to: On the Behavior of Singularities at the F-pure Threshold,
with Alessandro De Stefani, Zhibek Kadyrsizova, Robert Walker, George Whelan; paper by Eric Canton, Daniel Hernández, Karl Schwede, Emily Witt,
Illinois Journal of Mathematics, 60 (2016), no. 3–4, 669–685.
7. Mapping Toric Varieties into Low Dimensional Spaces,
with Emilie Dufresne,
to appear in Transactions of the American Mathematical Society, 28 pp.
8. Local Okounkov Bodies and Limits in Prime Characteristic,
with Daniel J. Hernández,
Mathematische Annalen, 372 (2018), no. 1, 139–178.
9. Polarization of Neural Ideals,
with Sema Güntürkün and Jeffrey Sun,
submitted. 15 pp.
10. A Zariski-Nagata Theorem for Smooth ℤ-Algebras,
with Alessandro De Stefani and Eloísa Grifo,
to appear in Journal für die reine und angewandte Mathematik, 14 pp.
11. Derived Functors of Differential Operators,
submitted, 12 pp.
12. Algebraic Signatures of Convex and Non-convex Codes,
with Carina Curto, Elizabeth Gross, Katherine Morrison, Zvi Rosen, Anne Shiu, and Nora Youngs,
submitted, 22 pp.

Department of Mathematics | University of Michigan | 2074 East Hall | 530 Church Street | Ann Arbor, MI 48109-1043