Jack Jeffries | Research

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Research

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, Math. Res. Lett., 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, J. Commut. Algebra, 7 (2015), no. 2, 189-206.
3. Multiplicities of Classical Varieties, with Jonathan Montaño and Matteo Varbaro, Proc. London Math. Soc., 110 (2015), no. 4, 1033-1055.
4. Separating Invariants and Local Cohomology, with Emilie Dufresne, Adv. Math., 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 J. Appl. Algebra Geom., 1 (2017), no. 1, 222-238.
6. Appendix to: On the Behavior of Singularities at the F-pure Threshold, with Alessandro De Stefani, Jack Jeffries, Zhibek Kadyrsizova, Robert Walker, George Whelan; paper by Eric Canton, Daniel Hernández, Karl Schwede, Emily Witt, Illinois J. Math., 60 (2016), no. 3, 669-685.
7. Mapping Toric Varieties into Low Dimensional Spaces, with Emilie Dufresne, to appear in Trans. Amer. Math. Soc., 28 pp.
8. Local Okounkov Bodies and Limits in Prime Characteristic, with Daniel J. Hernández, submitted. 47 pp.
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, submitted. 14 pp.




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

\[\mathrm{Hom}_R(\mathrm{Ext}_R^{d-i}(M,\omega_R),E_R(R/\mathfrak{m}))\cong \mathrm{H}^i_{\mathfrak{m}}(M)\] "When obliged to clean birds, collectors will find it an advantage to use salt and water instead of plain water. The salt prevents the solution of the blood-globules and consequent diffusion of the red haemoglobin."
J. Jeffries, Science, 1883