Thomas Polstra
Thomas Polstra
Office: 131 Kerchof Hall
Email: tp2tt@virginia.edu
Curriculum Vitae
About me
I am a research associate and lecturer at the University of Virginia. Before joining the math department at the University of Virginia
I was a National Science Foundation postdoctoral fellow at the University of Utah and prior to that I was a graduate student at the University of Missouri.
Research
I am a commutative algebraist. Commutative algebra is to algebraic geometry as analysis is to differential geometry.
In other words, commutative algebra is the local theory of algebraic geometry.
I typically devote my attention to problems of commutative algebra, but
I always keep in mind that the subjects of commutative algebra and algebraic
geometry are intertwined and as an algebraist it is beneficial to be motivated by geometric considerations, techniques, and results.
A primary goal of my research is to understand, measure, and relate singularities appearing
in prime characteristic algebraic geometry and commutative algebra. Motivation to do
so stems from algebraic techniques surrounding the theory of tight closure, geometric considerations
of birational geometry, and classical results concerning traditional measurements
of singularities.
Publications and preprints

Fsingularities: a commutative algebra approach (preliminary version), with Linquan Ma,
preliminary version.

Fpurity deforms in QGorenstein rings, with Austyn Simpson,
submitted.

Compatible ideals in Gorenstein rings, with Karl Schwede,
submitted.

Local cohomology bounds and test ideals, with Ian Aberbach,
submitted.

Covers of rational double points in mixed characteristic, with Javier CarvajalRojas, Linquan Ma, Kevin Tucker, and Karl Schwede,
submitted.

Global Fsplitting ratio,with Alessandro De Stefani and Yongwei Yao,
submitted.

A theorem about maximal CohenMacaulay modules,
to appear in Int. Math. Res. Not.

Global Frobenius Betti numbers and Euler characteristic, with Alessandro De Stefani and Yongwei Yao,
to appear in Mich. M. Journal.

Fnilpotent rings and permanence properties, with Jennifer Kenkel, Kyle Maddox, and Austyn Simpson,
to appear in J. Commutative Algebra.

Equimultiplicity theory of strongly Fregular rings,with Ilya Smirnov,
to appear in Mich. M. Journal.

Nilpotence of Frobenius actions on local cohomology and Frobenius closure of ideals, with Pham Hung Quy,
J. Algebra 529 (2019), 196225.

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

Continuity of HilbertKunz multiplicity and Fsignature, with Ilya Smirnov,
Nagoya Mathematical Journal, 124. doi:10.1017/nmj.2018.43.

Globalizing Finvariants, with Alessandro De Stefani and Yongwei Yao,
Adv. Math. 350 (2019), 359395.

Fsignature and HilbertKunz Multipicity: a combined approach and comparison, with Kevin Tucker,
Algebra & Number Theory 121 (2018), 6197.

Generalizing Serre's Splitting Theorem and Bass's Cancellation Theorem via freebasic elements,with Alessandro
De Stefani and Yongwei Yao,
Proc. Amer. Math. Soc. 146 (2018), no. 4, 14171430.

Uniform bounds in Ffinite rings and lower semicontinuity of the Fsignature,
Trans. Amer. Math. Soc. 370 (2018), no. 5, 31473169.

Depths and Stanley depths of path ideals of spines, with Daniel Campos, Susan Morey, and Chelsey Paulsen,
Involve, 9(1): 155170, 2016.

Depths and CohenMacaulay Properties of Path Ideals, with Daniel Campos, Susan Morey, and Chelsey Paulsen,
Journal of Pure and Applied Algebra, 218: 15371543, 2014.
Teaching
At the University of Virginia
MATH 1320, Calculus II, Fall 2020.
MATH 1310, Calculus I, Spring 2021.
At the University of Utah
MATH 4800, Undergraduate Research Mathematics, Fall 2019.
MATH 1260, Honors multivariable calculus, Fall 2018.
At the University of Missouri
MATH 8411 (Algebra II), Teaching Assistant, Spring 2016, Spring 2017.
MATH 8410 (Algebra I), Teaching Assistant and Reciatation Instructor, Fall 2016.
MATH 4720 (Introduction to Abstract Algebra) Recitation Instructor, Spring 2015, Fall 2015,
Spring 2017.
MATH 4140 (Matrix Theory) Instructor, Summer 2015, Summer 2017.
MATH 3000 (Introduction to Advanced Mathematics) Recitation Instructor, Fall 2016.
MATH 2320 (Discrete Mathematical Structures) Instructor, Spring 2017.
MATH 2300 (Calculus III) Instructor, Summer 2014, Summer 2016.
MATH 1700 (Calculus II) Recitation Instructor, Fall 2015.
MATH 1100 (College Algebra) Instructor, Fall 2013, Fall 2014.
MATH 0110 (Intermediate Algebra) Instructor, Spring 2014.