Thomas Polstra

Bertini’s Theorem for F-rationality is false (opens in a new tab)

with Austyn Simpson

Bertini’s Theorem for F-rational and F-pure singularities (opens in a new tab)

with Alessandro De Stefani and Austyn Simpson

F-injectivity does not imply F-fullness in normal domains (opens in a new tab)

with Alessandro De Stefani and Austyn Simpson

Strong F-regularity and the Uniform Symbolic Topology Problem (opens in a new tab)

Zariski–Nagata Theorems for Singularities and the Uniform Izumi–Rees Property (opens in a new tab)

To appear in Compositio Mathematica.

On the applications of Big Cohen–Macaulay Modules and Algebras

To appear in the AMS Contemporary Mathematics volume Lectures on Tight Closure and Its Applications.

On F-pure Inversion of Adjunction (opens in a new tab)

with Austyn Simpson and Kevin Tucker

Part of Higher Dimensional Algebraic Geometry—a volume in honor of V. V. Shokurov.

On the Equality of Test Ideals (opens in a new tab)

with Ian Aberbach and Craig Huneke

Adv. Math. (2024).

Local Cohomology Bounds and the Weak Implies Strong Conjecture in dimension 4 (opens in a new tab)

with Ian Aberbach

J. Algebra 605 (2022), 37–57.

F-singularities: a commutative algebra approach (preliminary version) (opens in a new tab)

with Linquan Ma

Preliminary version.

F-purity deforms in Q-Gorenstein rings (opens in a new tab)

with Austyn Simpson

Int. Math. Res. Not. IMRN (2023), no. 24.

Compatible ideals in Gorenstein rings (opens in a new tab)

with Karl Schwede

Proc. Amer. Math. Soc. (2023).

Local cohomology bounds and test ideals (opens in a new tab)

with Ian Aberbach

Permanent preprint due to delay of publication.

Global F-splitting ratio (opens in a new tab)

with Alessandro De Stefani and Yongwei Yao

J. Algebra 610 (2022), 773–792.

Covers of rational double points in mixed characteristic (opens in a new tab)

with Javier Carvajal-Rojas, Linquan Ma, Kevin Tucker, and Karl Schwede

J. Singul. 23 (2021), 127–150.

A theorem about maximal Cohen–Macaulay modules (opens in a new tab)

Int. Math. Res. Not. IMRN 2022, no. 3, 2086–2094.

Global Frobenius Betti numbers and Euler characteristic (opens in a new tab)

with Alessandro De Stefani and Yongwei Yao

Michigan Math. J. 71 (2022), no. 3, 533–552.

F-nilpotent rings and permanence properties (opens in a new tab)

with Jennifer Kenkel, Kyle Maddox, and Austyn Simpson

J. Commut. Algebra 15 (2023), no. 4, 559–575.

Equimultiplicity theory of strongly F-regular rings (opens in a new tab)

with Ilya Smirnov

Michigan Math. J. Advance Publication 1–20, 2021.

Nilpotence of Frobenius actions on local cohomology and Frobenius closure of ideals (opens in a new tab)

with Pham Hung Quy

J. Algebra 529 (2019), 196–225.

F-signature under birational morphisms (opens in a new tab)

with Linquan Ma, Karl Schwede, and Kevin Tucker

Forum Math. Sigma 7 (2019), e11, 20 pp.

Continuity of Hilbert–Kunz multiplicity and F-signature (opens in a new tab)

with Ilya Smirnov

Nagoya Mathematical Journal, 1–24. doi:10.1017/nmj.2018.43.

Globalizing F-invariants (opens in a new tab)

with Alessandro De Stefani and Yongwei Yao

Adv. Math. 350 (2019), 359–395.

F-signature and Hilbert–Kunz Multiplicity: a combined approach and comparison (opens in a new tab)

with Kevin Tucker

Algebra & Number Theory 12-1 (2018), 61–97.

Generalizing Serre’s Splitting Theorem and Bass’s Cancellation Theorem via free-basic elements (opens in a new tab)

with Alessandro De Stefani and Yongwei Yao

Proc. Amer. Math. Soc. 146 (2018), no. 4, 1417–1430.

Uniform bounds in F-finite rings and lower semi-continuity of the F-signature (opens in a new tab)

Trans. Amer. Math. Soc. 370 (2018), no. 5, 3147–3169.

Depths and Stanley depths of path ideals of spines (opens in a new tab)

with Daniel Campos, Susan Morey, and Chelsey Paulsen

Involve 9(1) (2016), 155–170.

Depths and Cohen–Macaulay Properties of Path Ideals (opens in a new tab)

with Daniel Campos, Susan Morey, and Chelsey Paulsen

Journal of Pure and Applied Algebra 218 (2014), 1537–1543.