I am an assistant professor in the mathematics department at the University of Alabama. Prior to my current position, I was a Simons postdoctoral fellow at MSRI, research associate and lecturer at the University of Virginia, NSF postdoctoral fellow at the University of Utah, and a graduate student at the University of Missouri.

Publications and Preprints

Strong F-regularity and the Uniform Symbolic Topology Propblem,
Submitted.

Zariski-Nagata Theorems for Singularities and the Uniform Izumi-Rees Property,
Submitted.

On F-pure Inversion of Adjunction, with Austyn Simpson and Kevin Tucker
accepted to Shokurov’s 70th birthday volume.

Primary Decompositions of Regular Sequences,
submitted.

On the Equality of Test Ideals, with Ian Aberbach and Craig Huneke,
Adv. Math. (2024).

Local Cohomology Bounds and the Weak Implies Strong Conjecture in dimension 4, with Ian Aberbach,
J. Algebra 605 (2022), 37–57.

F-singularities: a commutative algebra approach (preliminary version), with Linquan Ma,
preliminary version.

F-purity deforms in Q-Gorenstein rings, with Austyn Simpson,
Int. Math. Res. Not. IMRN (2023), no.~24.

Compatible ideals in Gorenstein rings, with Karl Schwede,
Proc. Amer. Math. Soc. (2023).

Local cohomology bounds and test ideals, with Ian Aberbach,
permanent preprint due to delay of publication.

Global F-splitting ratio,with Alessandro De Stefani and Yongwei Yao,
J. Algebra 610 (2022), 773–792.

Covers of rational double points in mixed characteristic, with Javier Carvajal-Rojas, Linquan Ma, Kevin Tucker, and Karl Schwede,
J. Singul. 23 (2021), 127–150.

A theorem about maximal Cohen-Macaulay modules,
Int. Math. Res. Not. IMRN 2022, no. 3, 2086–2094.

Global Frobenius Betti numbers and Euler characteristic, with Alessandro De Stefani and Yongwei Yao,
Michigan Math. J. 71 (2022), no. 3, 533--552.

F-nilpotent rings and permanence properties, with Jennifer Kenkel, Kyle Maddox, and Austyn Simpson,
J. Commut. Algebra 15 (2023), no. 4, 559--575.

Equimultiplicity theory of strongly F-regular rings,with Ilya Smirnov,
Michigan Math. J. Advance Publication 1 - 20, 2021.

Nilpotence of Frobenius actions on local cohomology and Frobenius closure of ideals, with Pham Hung Quy,
J. Algebra 529 (2019), 196--225.

F-signature under birational morphisms, with Linquan Ma, Karl Schwede, and Kevin Tucker,
Forum Math. Sigma 7 (2019), e11, 20 pp.

Continuity of Hilbert-Kunz multiplicity and F-signature, with Ilya Smirnov,
Nagoya Mathematical Journal, 1-24. doi:10.1017/nmj.2018.43.

Globalizing F-invariants, with Alessandro De Stefani and Yongwei Yao,
Adv. Math. 350 (2019), 359--395.

F-signature and Hilbert-Kunz Multipicity: a combined approach and comparison, 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,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,
Trans. Amer. Math. Soc. 370 (2018), no. 5, 3147--3169.

Depths and Stanley depths of path ideals of spines, with Daniel Campos, Susan Morey, and Chelsey Paulsen,
Involve, 9(1): 155-170, 2016.

Depths and Cohen-Macaulay Properties of Path Ideals, with Daniel Campos, Susan Morey, and Chelsey Paulsen,
Journal of Pure and Applied Algebra, 218: 1537-1543, 2014.

Thomas Polstra

Publications and Preprints

Teaching

Teaching at the University of Alabama

At the University of Virginia

At the University of Utah

At the University of Missouri