Tom Marley's Homepage
203 Avery Hall
Department of Mathematics
University of Nebraska-Lincoln
Lincoln, NE 68588-0130
Phone: (402) 472-7260
FAX: (402) 472-8466
Teaching (Fall 2018)
Math 107H (Honors Calculus II): MWF 9:30-10:20 in BL 206
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
Below are some of my publications:
- Hilbert coefficients and the depths of associated
graded rings , joint with Sam Huckaba, Journal of the
London Math. Soc (2) 56 (1997) 64-76.
- Cofinite modules and local cohomology , joint
with Donatella Delfino, Journal of Pure and Applied Algebra
121 (1997) 45-52.
- On associated graded rings of normal ideals , joint
with Sam Huckaba, Journal of Algebra 222 (1999), 146-163.
- The associated primes of local cohomology modules over
rings of small dimension , Manuscripta Mathematica 104 (2001), 519-525.
- Cofiniteness and associated primes of local
cohomology modules , joint with Janet Vassilev, Journal of Algebra 256 (2002), 180-193.
- Local cohomology modules with infinite dimensional
socles , joint with Janet Vassilev, Proc. of the American Math. Soc 132 (2004), 3485-3490.
- Non-Noetherian Cohen-Macaulay rings , joint with Tracy Hamilton, Journal of Algebra 307 (2007), 343-360.
- On rings for which finitely generated ideals have only finitely many minimal components, Communications
in Algebra 35 (2007), no. 5, 1757-1760.
- Gorenstein rings and irreducible parameter ideals, joint with Mark Rogers and Hideto Sakurai, Proc. Amer. Math. Soc. 136, no. 1 (2008),
- On the support of local cohomology, joint with Craig Huneke and Daniel Katz,
Journal of Algebra 322 (2009), no. 9, 3194-3211.
- The Auslander-Bridger formula and the Gorenstein property for coherent rings, joint with
Livia (Miller) Hummel, Journal of Commutative Algebra 1 (2009), no. 2, 283-314.
- The Frobenius functor and injective modules, Proceedings of the American Math. Soc. 142 (2014), no. 6, 1911-1923.
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, to appear in Journal of Commutative Algebra.
- Characterizing Gorenstein rings using contracting endomorphisms, joint with Brittney Falahola, to appear in Journal of Algebra.
- Frobenius and homological dimensions of complexes, joint with Taran Funk, preprint.
Slides from recent talks:
- Frobenius and injective modules, Riverside AMS meeting, November 2013.
- Cohen-Macaulay dimension for coherent rings, Albuquerque AMS meeting, April 2014.
- Frobenius and modules of finite flat dimension, San Antonio JMM meeting, January 2015.
- 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.
- 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
- Doug Dailey, PhD 2016
- Becky Egg, PhD 2016
- Brittney Falahola, PhD 2017
- Taran Funk, current student.
Links of Interest