Willa Cather Professor Emeritus Profile Image
Willa Cather Professor Emeritus Mathematics rwiegand@unl.edu 329 Avery Hall

CV and Publication List


Contact Information

Mailing Address:
329 Avery Hall
Department of Mathematics
University of Nebraska-Lincoln
Lincoln, NE 68588-0130

FAX: 402-472-8466

Home Address:
2400 Sheridan Blvd
University of Nebraska-Lincoln
Lincoln, NE 68502-4042

Phone: 402-476-7260

Summer Address:
PO Box 132
Glen Haven, CO 80532

Cell Phone: 402-613-5581

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, and representation theory. Graham Leuschke's and my book Cohen-Macaulay Representations appeared in 2012, in the American Mathematical Society's Surveys and Monographs series.

Below are links to some of my publications and erreta:


Errata:

  • The paper "Tensor products of modules and the rigidity of Tor" (by C. Huneke and R. Wiegand, Math. Ann. 299 (1994), 449--476) has errors caused by an incorrect convention concerning the depth of the zero module. These errors do not affect the validity of the main results of the paper, but several proofs need to be modified. See the erratum for details.
  • The paper "Bounds for one-dimensional rings with finite Cohen-Macaulay type" (by R. Wiegand and S. Wiegand, J. Pure Appl. Algebra 93 (1994), 311-342) asserts, in Example 3.12, that there is a local one-dimensional ring with finite Cohen-Macaulay type, having a finitely generated indecomposable torsion-free module of rank 4. Nicholas Baeth has shown, in Section 6 of his paper A Krull-Schmidt for one-dimensional rings of finite Cohen-Macaulay Type, MR 2283435, that the module in question is in fact a direct sum of two modules of rank two. In fact, his results imply, at least in the equicharacteristic-zero case, that the sharp bound on the ranks of the indecomposables is three. One of the main results of the Wiegand /Wiegand paper is that, over a one-dimensional ring (not necessarily local) with bounded Cohen-Macaulay type, each indecomposable torsion-free module has rank 1, 2, 3, 4, 5, 6, 8, 9 or 12. In view of Baeth's results, it is likely that the list can be shortened to the following: 1, 2, 3, 4 or 6, though this has not been worked out in full generality. The construction, in Section 5 of the Wiegand/Wiegand paper, of indecomposable modules (in the non-local case) of ranks 5, 7, 8, 9 and 12, is invalid, since it depends on the incorrect assertion in Example 3.12.
  • In the paper "Noetherian rings of bounded representation type", MR 1015536, Lemma 2.4 makes the ludicrous claim that the functor F (reduction modulo an ideal) preserves indecomposability of modules over Artinian pairs. (Consider, for example, the Artinian pair (k[t^3,t^7], k[t]), with t^12 = 0. This is the bottom line of the conductor square for the ring k[[T^3,T^7]], which has infinite representation type. Therefore the Artinian pair has indecomposable modules of arbitrarily large rank. If we take I = tk[t] in the statement of Lemma 2.4, the resulting Artinian pair is (k, k), which has only one indecomposable module. Letting (V,W) be an indecomposable module over (k[t^3,t^7], k[t]), with W free of rank >1, we see that F(V,W) must decompose.) Fortunately this claim is never used in the paper.

Meetings and Conferences

The following are links to conferences I have attended recently or expect to attend soon.


Ph.D. Students

  • Mohsen Gheibi (Ph.D. 2018, co-advised by Mark Walker; postdoc, University of Texas-Arlington)
  • Neil Steinburg (Ph.D. 2018, co-advised by Tom Marley; Visiting Assistant Professor, Drake University)
  • Katharine Shultis (Ph.D. 2015, co-advised by Srikanth Iyengar; Assistant Professor, Gonzaga University)
  • Courtney Gibbons (Ph.D. 2013, co-advised by Luchezar Avramov; Assistant Professor, Hamilton College)
  • Micah Leamer (Ph.D. 2011, co-advised by Srikanth Iyengar; Postdoctoral Scholar 2011-2012, Chennai Mathematical Institute)
  • Olgur Celikbas (Ph.D. 2010, co-advised by Mark Walker; Postdoctoral Scholar, University of Connecticut)
  • Silvia Saccon (Ph.D. 2010; Dean's Fellow, University of Texas-Dallas)
  • Andrew Crabbe (Ph.D. 2008; Postdoctoral Scholar, Syracuse University; currently attending Perelman School of Medicine)
  • Nicholas Baeth (Ph.D. 2005; Assoc. Professor, Central Missouri State University)
  • Ryan Karr (Ph.D. 2002; Associate Professor, University of Wisconsin-Parkside)
  • Karl Kattchee (Ph.D. 2001; Associate Professor, University of Wisconsin-LaCrosse)
  • Graham Leuschke (Ph.D. 2000; Professor, Syracuse University)
  • Darren Holley (Ph.D. May 1997; Faculty, Omaha North High School)
  • David Jorgensen (Ph.D. 1996; Professor, University of Texas-Arlington)
  • Kurt Herzinger (Ph.D. 1996; Professor, US Air Force Academy)
  • Nuri Cimen (Ph.D. 1994; Associate Professor, Hacettepe University)
  • Bao Ping Jia Bao Ping Jia (Ph.D. 1990; Associate Professor, Maryville University)
  • William W. Krauter (Ph.D. 1980; Software Engineer, Lockheed Martin)
  • Bette Midgarden (Ph.D. 1978; Professor, Minnesota State University-Moorhead)
  • Thomas S. Fischer (Ph.D. 1977; Kaiser Permanente (now retired)
This photo was taken by Olle Swartling at 4:50 p.m. on July 25, 1969, from the summit of Nevado Chinchey, 20,413', in the Cordillera Blanca, Peru. I'm on the left; Steve Moore is on the right.

I enjoy rock climbing and mountaineering (as you might guess from the photo). Check out some more pictures taken on an ascent of the Longs Peak Diamond during the summer of 2000. And here are some more recent pictures of some climbing in Provence, in March, 2009. Back in my youth I did a few 100-mile trail runs. One such adventure was the 1999 Hardrock Endurance Run.