The above generalizes to representation theory of groups. In particular, the representation theory of finite groups is well developed. In the second half of the previous century, ideas from this theory gave impetus to the development of representation theory in a more general context: that of finite dimensional algebras.
This project dealt with some of the most prominent open questions in representation theory of finite dimensional algebras. In particular, we investigated the homological conjectures of Bass and Nakayama from the 60s. We have applied computational methods, and part of the project dealt with further development of computer software (QPA = Quivers and path algebras). We also
applied and developed reduction techniques, motivated by the potential of generalizing ideas of cluster combinatorics to general finite dimensional algebras. Two PhD-students and a postdoctoral fellow were hired in the project.
The project has educated two PhD-students to obtain their doctoral degree at NTNU. The two hired candidates will defense their theses in October and November 2025. A postdoc was hired, who has recently obtained a three year mobility project grant from RCN (FriPro). The project has resultet in a high number of international publications, and the results will have a significant impact on the research field of Representation Theory of finite dimensional algebras and applications.
The main aim is to further develop and apply reduction techniques to prominent open problems in Representation theory.
There are three work packages.
WP1: Apply reduction techniques to study problems related to tau-tilting, motivated by the potiential of generalizing ideas of cluster combinatorics to general finite dimensional algebras.
WP2: Further develop and apply QPA to investigate problems concerning computiations of projective resolutions and in particular in determining the finiteness of projective dimension of modules.
WP3: Use computational methods and ideas from WP2 and reduction techniques studied in WP1, together
with other reduction techniques, to attack one of the long standing conjectures in representation theory: the finitistic dimension conjecture.
