Last updated: Oct. 6, 2004

Northeastern University
Mathematics Department

Maurice Auslander
Distinguished Lectures*

October 8 - 10, 2004

Maurice Auslander

1926 - 1994


Helmut Lenzing

Idun Reiten

Claus Michael Ringel

This year marks the tenth anniversary of Maurice Auslander's death. To commemorate this event, the speakers in the 2004 Distinguished Lectures will focus on the last decade's developments in representation theory related to Maurice's work. The Lectures will be embedded in the Conference on Representations of Algebras, to be held concurrently at Northeastern University on October 8 - 10. A small amount of money is available for travel expenses. Preference will be given to young researchers. To apply or for further information, please contact  Alex Martsinkovsky  <alexmart at neu dot edu>


All lectures will be given in 315 Behrakis

Date and time
Friday, Oct. 8,
4:00 - 5:00
Claus Michael Ringel (Bielefeld)
Auslander and the Brauer-Thrall conjectures
Saturday, Oct. 9, 4:00 - 5:00
Idun Reiten
Connections between work of Maurice and my recent work
Sunday, Oct. 10
11:30 - 12:30
Helmut Lenzing
Hereditary noetherian categories and singularities

Social Program

Date and Time
Friday, Oct. 8. 5:15 - 6:45
340 Egan
Friday, Oct. 8, 7:30

Registered Participants

Silvana Bazzoni
University of Padua
Ernst Dieterich
Uppsala University
Pavel Etingof
Martin Herschend
Uppsala University
Kiyoshi Igusa
Brandeis University
Mark Kleiner
Syracuse University
Helmut Lenzing
University of Paderborn
Shiping Liu
University of Sherbrooke
Francesca Mantese
University of Verona
Alex Martsinkovsky
Northeastern University
Izuru Mori
SUNY, Brockport
Idun Reiten
NTNU, Trondheim
Claus Michael Ringel
University of Bielefeld
Ralf Schiffler
Carleton University
Gordana Todorov
Northeastern University
Alberto Tonolo
University of Padua
Rita Zuazua
Institute of Mathematics, UNAM, Morelia

Titles and Abstracts

  • Helmut Lenzing (University of Paderborn), Hereditary noetherian categories and singularities
       Abstract: A remarkable result of Maurice Auslander establishes existence of almost split sequences for (a suitable category of modules over) an isolated singularity (and also a converse). We are going to link this question with the topic of hereditary noetherian categories which, due to the work of a number of authors, has attracted a lot of attention in recent years. In the case of a, possibly graded, surface singularity we investigate the category of coherent sheaves on the punctured (graded) spectrum of the singularity. Each such category is a hereditary, in particular abelian, category whose objects are noetherian and which satisfies Serre duality, in a sense to be specified.

In a related context we take up former studies of Auslander and Reiten on the completion from graded Cohen Macaulay modules over suitable graded rings to Cohen Macaulay modules over complete local rings and discuss properties of the completion functor, with a focus on factoriality.

  • Idun Reiten (NTNU, Trondheim), Connections between work of Maurice and my recent work
       Abstract: The emphasis of my lecture will be some work by (and with) Maurice, which has connections with some of my work (with various coauthors) during the last years, in particular on hereditary categories with Serre duality and cluster-tilted algebras. In the process we include some recent results with Buan and Marsh.

  • Claus Michael Ringel (University of Bielefeld), Auslander and the Brauer-Thrall conjectures
       Abstract: The first Brauer-Thrall conjecture for algebras was solved by Roiter in 1968, but his proof did not extend to artinian rings. In 1974, Auslander published a proof for the general case. This proof (partially modified by Yamagata) is now considered as the standard one and it may be considered as the basis of what is called the Auslander-Reiten theory. But it seems to be worthwhile to draw attention also to the original proof of Roiter and the influence it had. After all, it is clear that Auslander was strongly impressed by Roiter's approach, and he extended the scope of the methods of Roiter (and of the interpretation of these methods by Gabriel) considerably: let us mention his construction of indecomposables of infinite length, as well as his joint work with SmalÝ on preprojective and preinjective modules.

The lecture will focus the attention on these developments in  representation theory of algebras. In particular, we also want to draw attention to Auslander's interest in the second Brauer-Thrall conjecture and the trichotomy of finite, tame, and wild representation type: in 1993 a workshop was held - on his request - at the Bielefeld SFB dealing with these questions...

Archive: 2003 2002

* Sponsored by Bernice Auslander