Position

Professor and Dale Jensen Chair of Mathematics
University of Nebraska-Lincoln

Contact Information

Office: 329 Avery Hall
email: tmarley1@unl.edu

Teaching (Fall 2025)

Math 208:  Calculus III, MWF 12:30-1:20 in Morr 141.
Math 915:  Homological Algebra , MWF 11:30-12:20 in AvH 111.
Office hours: TBA

Research

My research interests lie in the field of commutative algebra, a branch of mathematics focused on the study of algebraic equations and their solutions. The field has its origins in number theory, algebraic geometry, and invariant theory.

Below are some of my recent publications:


• The acyclicity of the Frobenius functor for modules of finite flat dimension, joint with Marcus Webb, J. Pure Appl. Algebra 220 (2016), 2886-2896.
  
  
• A change of rings result for Matlis reflexivity, joint with Douglas Dailey, Proc. American Math. Soc. 145 (2017), no. 5, 1837-1841.
  
  
• Rigidity of Ext and Tor with coefficients in residue fields of a commutative noetherian ring, joint with Lars Christensen and Sri Iyengar, Proceedings of the Edinburgh Math. Soc. 62 (2019), 305-321.
  
  
• Detecting finite flat dimension of modules via iterates of the Frobenius endomorphism, joint with Douglas Dailey and Sri Iyengar, Journal of Commutative Algebra 12 (2020), no. 1, 71-76.
  
  
• Characterizing Gorenstein rings using contracting endomorphisms, joint with Brittney Falahola, Journal of Algebra 571 (2021), 168-178.
  
  
• Frobenius and homological dimensions of complexes, joint with Taran Funk, Collectanea Mathematica 71 (2020), no. 2, 287-297.
  
  
• Levels and Gorenstein projective dimension, joint with Laila Awadalla, Journal of Algebra 609 (2022), 606-618.


Slides from recent talks:


• The beauty, mystery, and utility of prime numbers, talk given to high school students at the University of New Mexico, February 2015.
• The Binomial theorem without middle terms: putting prime numbers to work in algebra, Missouri MAA meeting in St. Joseph, MO, April 2016.
• Matlis reflexivity and change of rings, Charleston AMS meeting, March 2017.
• Characterizing Gorenstein rings using the Frobenius endomorphism, Denton AMS meeting, September 2017.
• Frobenius and homological dimensions, Honolulu AMS meeting, March 2019.
• Levels and Gorenstein projective dimension, Cincinnati AMS meeting, April 2023.


Miscellaneous Stuff:


• Graded rings and modules. These are some notes based on a five-week course I taught in the summer of 1993.
• Introduction to local cohomology. These are notes from a 1999 summer course. The notes were recently put into LaTeX by Laura Lynch.
• Math 901/902. These are notes created by Robert Huben on the Math 901-902 course I taught in 2015-16.
• The Homological Conjectures. These are notes on a course given in the spring semester, 2009. Laura put these notes into LaTeX as well.
• Class notes for Math 906 (Commutative Algebra II), Spring semester 2024.

PhD Students

• Victoria Sapko, PhD 2001
• Ed Loeb, PhD 2006
• Livia Hummell, PhD 2008
• Laura Lynch, PhD 2011
• Lori McCune, PhD 2011
• Brian Johnson, PhD 2012
• Marcus Webb, PhD 2015
• Douglas Dailey, PhD 2016
• Rebecca Egg, PhD 2016
• Brittney Falahola, PhD 2017
• Taran Funk, PhD 2021.
• Laila Awadalla, PhD 2022
• Zach Nason, current student
• Sara Mueller, current student
• Abbey Moos, current student