Below are links for files of preprints some research manuscripts. (The order is roughly reverse chronological.) The author's research papers on this site were all prepared while the author was partially supported by grants from the National Science Foundation. The current grant is DMS-1902116 and the two most recent previous grants were DMS-1401384 and DMS-0901145. If papers have appeared, the preprint version here is usually not identical with the published version.

Frobenius splitting, strong F-regularity, and small Cohen-Macaulay modules (with Y.Yao), preprint, February, 2022.

A Jacobian criterion for nonsingularity in mixed characteristic (with J. Jeffries), preprint, June, 2021.

F-rational signature and drops in the Hilbert-Kunz multiplicity (with Y. Yao), Algebra & Number Theory, to appear.

Extensions of primes, flatness, and intersection flatness (with J. Jeffries), in "Commutative Algebra: 150 years with Roger and Sylvia Wiegand," Contemporary Mathematics Volume 773 , 2021, 63-81.

Faithfulness of top local cohomology modules in domains (with J. Jeffries), Math. Res. Letters 27 (2020) 1755-1765.

The Eisenbud-Green-Harris conjecture for defect two quadratic ideals (with S. Güntürkün), Math. Res. Lett. Math. 27 (2020) 1341--1365.

Universal lex approximations of extended Hilbert functions and Hamilton numbers (with T. Ananyan), Journal of Algebra 560 (2020), 4757-4806;

Strength conditions, small subalgebras, and Stillman bounds in dimension ≤ 4 (with T. Ananyan), Trans. of the Amer. Math. Soc. 373 (2020) 4547-4806; Corrigendum , 374 (2021), 8307-8308.

Small subalgebras of polynomial rings and Stillman's conjecture (with T. Ananyan), Journal of the Amer. Math. Soc. 33 (2019) 291-309.

Content of local cohomology, parameter ideals, and robust algebras (with W. Zhang), Trans. Amer. Math. Soc. 370 (2018), 7789-7814.

Continuous closure, natural closure, and axes closure, (with N. Epstein), Trans. Amer. Math. Soc. 370 (2018), 3315-3362.

On the support of local cohomology via Frobenius (with L. Núñez-Betancourt), Math. Res. Letters 24 (2017) 401-420.

F-purity, Frobenius splitting, and tight closure, volume on Commutative Algebra honoring David Eisenbud, 471-484, Springer, NY, 2013.

Local cohomology with support in a parameter ideal (with Y. Yao), J. Pure and Applied Algebra 217 (2013) 664-671.

Test exponents for modules with finite phantom projective dimension (with Y. Yao), Illinois J. Math. 56 (2012) 1095-1107.

Ideals generated by quadratic polynomials (with Tigran Ananayan), Math. Res. Letters, 19 (2012) 233-244.

Homological invariants of modules over contracting endomorphisms (with L. Aramov, S. Iyengar, and Y. Yao), Math. Annalen, 353 (2012), 275-291.

An embedding theorem for modules of finite projective dimension (with Y. Yao).

Second coefficients of Hilbert-Kunz functions for domains (with Y. Yao).

Tight closure in equal characteristic zero   (with C. Huneke, 204 pages).

Quasilength, latent regular sequences, and content of local cohomology (with C. Huneke), Journal of Algebra 322 (2009) 3170-3193.

The Frobenius structure of local cohomology, (with F. Enescu), Algebra & Number Theory 2 (2008) 721-754.

Fine behavior of symbolic powers of ideals (with C. Huneke) Illinois J. Math. 51 (2007), 171--183.

Some finiteness properties of Lyubeznik's F-modules, Proceedings of the Midwest Algebraic Geometry Seminar, 2005 (MAGIC05) Contemp. Math 448. Amer. Math. Soic., Providence, R.I., 2007, 119-127.

Lower bounds for Betti numbers of special extensions   (with B. Richert), Journal of Pure and Applied Algebra 201 (2005) 328-339.

Diamond closure   (with J. Velez), in Algebra, Arithmetic and Geometry with Applications, Papers from Shreeram S. Abhyankar's 70th Birthday Conference, Springer-Verlag, Berlin - Heidelberg - New York, 2004, pp. 511-523.

Parameter-like sequences and extensions of tight closure   in Commutative Ring Theory and Applications (Proc. of the Fourth International Conference, held in Fez, Morocco, June 7-12, 2001), Marcel Dekker, New York, 2003, pp. 267-287.

Big Cohen-Macaulay algebras in dimension three via Heitmann's theorem,   Journal of Algebra 254 (2002) 395-408.

Presentation depth and the Lipman-Sathaye Jacobian Theorem,   Homology, Homotopy and Applications (International Press, Cambridge, MA) Vol. 4 (2002) 295-314.

Comparison of symbolic and ordinary powers of ideals   (with C. Huneke), Inventiones Math. 147 (2002) 349-369.

Localization and test exponents for tight closure  (with C. Huneke), Michigan Math. J. 48 (2000) 305-329.

The tight integral closure of a set of ideals,   J. of Algebra 230 (2000) 184-203.

Failure of coherence and finite Tor dimension in absolute integral closures   (with Ian M. Aberbach), Journal of Pure and Applied Algebra (memorial issue for H. Matsumura) 122 (1997), 171-184.

Solid Closure,   in Commutative Algebra: Syzygies, Multiplicities and Birational Algebra, Contemp. Math. 159, Amer. Math. Soc., Providence, R. I., 1994, 103-172.

F-regularity, test elements, and smooth base change   (with C. Huneke), Trans. Amer. Math. Soc. 346 (1994), 1-62.

Indecomposable canonical modules and connectedness   (with C. Huneke), in Commutative Algebra: Syzygies, Multiplicities and Birational Algebra, Contemp. Math. 159, Amer. Math. Soc., Providence, R. I., 1994, 197-208.

Absolute integral closures are big Cohen-Macaulay algebras in characteristic p   (with
C. Huneke), Bull. Amer. Math. Soc. (New Series) 24 (1991), 137-143.