Department of Mathematical Sciences


The group's research activity is mostly oriented towards theoretical studies of algebraic questions, but members of the group also work on more applied topics related to cryptography.

Research Activity

The research activity within the theoretical side of the algebra group consists mainly of

  • representation theory of algebras
  • homological algebra, including Hochschild cohomology
  • triangulated and derived categories
  • Lie algebras
  • commutative algebra
  • algebraic geometry
  • connections between geometry and representation theory

A part of the group has been working on topics related to cluster algebras, which was introduced a few years ago and have many interesting connections to different parts of algebra and other areas of mathematics. Hochschild cohomology, Koszul algebras, support varieties of module categories and triangulated categories (and connections between these) are all active research topics today.


The cryptographic research consists mostly of cryptographic protocol analysis.

One project studies anonymous communications and payment, which also involves theoretical work on how to prove protocols secure and how to increase confidence in the correctness of those proofs.

Another more applied line of research relates to electronic voting and identification, where we have contributed analysis of (to-be-)deployed systems.

Members of the group have also worked on the application of elliptic curves to cryptography, most recently on the use of bilinear pairings in cryptography.


Øyvind Solberg. Photo. Professor Øyvind Solberg, Head of the Algebra group


Staff – Algebra group


Current Projects

Completed Projects

Recent Publications

Claire Amiot, Osamu Lyama and Idun Reiten
Stable categories of cohen-macaulay modules and cluster categories: Dedicated to Ragnar-Olaf Buchweitz on the occasion of his sixtieth birthday
American Journal of Mathematics

Kristin Krogh Arnesen and Yvonne Grimeland
The Auslander-Reiten components of K^b(proj A) for a cluster-tilted algebra of type Ã
Journal of Algebra and its Applications

Thomas Brustle and Yu Qiu
Tagged mapping class groups: Auslander–Reiten translation
Mathematische Zeitschrift

Karin Marie Jacobsen and Benedikte Grimeland
Abelian quotients of triangulated categories
Journal of Algebra

Alastair King and Yu Qiu
Exchange graphs and Ext quivers
Advances in Mathematics

Steffen Oppermann, Idun Reiten and Hugh Thomas
Quotient closed subcategories of quiver representations
Compositio Mathematica

Yu Qiu
Stability conditions and quantum dilogarithm identities for Dynkin quivers
Advances in Mathematics

View all publications