## The theme

If one deals with artin algebras and their module categories one feels
that those of finite global dimension seem to be the most accessible ones.
Indeed, artin algebras of global dimension at most 1, the hereditary algebras,
are quite well understood. However, aready for global dimension 2,
one gets stuck: one knows
a lot of examples (but they are not yet sorted), and one observes that
there are algebras with quite different behaviour: of course, there
are the tilted algebras and the quasi-hereditary algebras
of global dimension 2, but they seem to be well-behaved. In general
one may look at the tensor algebra of the A-A-bimodule Ext^{2}(DA,A),
note
that this algebra may be infinite dimensional even for quasi-hereditary
algebras. Looking at various conjectures
in the representation theory of artin algebras, it turns out that many
are not settled even in the case of projective dimension 2.
The workshop is devoted to the presentation of examples of the strange
behaviour of some artin algebras of global dimension 2, to general
problems where already the restriction to dimension 2 is open, and to
proposals how a structure theory of these artin algebras and their
module categories may look like.

The present schedule includes an overview on the difficulties
of projective dimension 2 by Dieter **Happel**, and lectures by
Idun **Reiten**, Steffen **Oppermann**,
Winfried **Bruns**, Sefi **Ladkani**, and Helmut **Lenzing.**

Anyone interested in the subject is invited to participate.
Short (or longer) contributions are very well-come, please contact C.M.Ringel
(ringel@math.uni-bielefeld.de).
Financial support can be provided by the
CRC 701, Bielefeld, please contact C.M.Ringel
(ringel@math.uni-bielefeld.de).

If you like to participate, we would appreciate that you send
a short message to ringel@math.uni-bielfeld.de. Please
indicate whether you will join the dinner.

The aim of the workshop is to collect (and make available)
as much information and questions as possible.

Anyone is invited to provide suitable
material on the topic,
in the same way as it was done at several previous Bielefeld
workshops.

Since the workshop has been announced on a very short notice,
we cannot expect too many
visitors from abroad, thus there is been the proposal
that it may be used as a preparation for a slightly
larger meeting early next year (either in Bielefeld
or as part of the Bonn activities).