Network: Invariants and Representations of Algebras

UIA Antwerp, Bielefeld-Chemnitz, Edinburgh-Glasgow, Essen, Ioannina, Leeds, Murcia, Paris VI, Torun, Trondheim

Euroconferences 1996-1999: Aims

Associative algebras and their representations play an important role in mathematics; many topics in algebra and geometry, but also in analysis may be reformulated and solved in this way. The Hall algebra approach to quantum groups shows that structural results in representation theory may have surprising consequences in mathematical physics. Representation theory of algebras is a rapidly evolving area of research with many interrelations to other parts of mathematics.

The aim of representation theory is to provide a unified approach to the possible operations of algebras on vector spaces. The study of algebras relies on the possibility of being able to distinguish algebras by suitable invariants. The classification problems in representation theory can be approached using geometrical and homological considerations: Often one obtains combinatorial invariants which allow the use of computers. The progress in the representation theory of algebras has to be considered as a corner-stone of the development of a general topic Noncommutative Algebraic Geometry.

There exists a European network of leading laboratories devoted to the study of representations and invariants of algebras. It was established under the SCIENCE and the HCM scheme and it is organizing in the next three years four Euroconferences devoted to the main aspects of the theory.

  1. The first conference planned will focus attention on the use of computers in representation theory, it will be held at the Institute for Experimental Mathematics in Essen (1996 or 1997) and will serve as a platform for outlining the up-to-date methods in computational representation theory of groups and algebras. At the meeting there will be demonstrations of the use of advanced computer algebra systems and related packages.
  2. The second conference will be held at Murcia (Spain). It will be devoted to the ring theoretical (Murcia 1997) in representation theory. This serves to spread the existing knowledge and to provide an efficient training for young researchers.
  3. One of the most intriguing problem in representation theory is the interrelation between finite and infinite dimensional modules (as the open problem of understanding the tameness of algebras shows). This topic and its relationship to model theory and algebraic geometry will be the central theme of the third conference (Bielefeld 1998).
  4. The last conference will be held near Ioannina (Greece) and will be devoted to homological methods in representation theory.

The aim of these conference is to spread the existing knowledge and to provide an efficient training for young researchers. The planned Euroconferences rely mainly on the specific expertise and competence of the participating teams of the network; in addition some experts from other European universities as well as mathematicians from the U.S., Israel and Japan will be invited as keynote speakers. The aim of these Euroconferences is to bring together the main experts and to provide an intense research training for young researchers interested in invariants and representations of algebras. In addition, researchers working in other parts of mathematics can use this opportunity to obtain expertise in representation theory for applications in their subjects.

The four Euroconferences form a unit. The various aspects of the representation theory of algebras which will be high-lighted have to be seen together. Together, these conferences and the corresponding proceedings which will be published shall provide a clear overview on the present state of knowledge and in this way, it will stream-line the further development of the subject.

28.6.1996 Last modified: 28.8.1996

The four Euroconferences organized by the Network "Invariants and Representations of Algebras".