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

* Extensions of primes, flatness, and intersection flatness
* ** (with J. Jeffries), to appear in "Commutative Algebra: 150 years with Roger and Sylvia Wiegand," Amer. Math. Soc., Providence, RI.
**

* 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.
**

* 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).
**

**
The F-rational signature and drops in the Hilbert-Kunz multiplicity (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.
**