Algebra

Algebra

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.

Cryptography

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.

Projects

Projects

Current projects

Completed projects

Conferences and workshops

Conferences and workshops

Upcoming

Previously held

Recent publications

Recent publications

Aslak Bakke Buan
From classical tilting to two-term silting
Science China Mathematics

Lars Winther Christensen, Sergio Estrada and Peder Thompson
Homotopy categories of totally acyclic complexes with applications to the flat-cotorsion theory
Contemporary Mathematics

Katriel Cohn-Gordon, Cas Cremers, Kristian Gjøsteen, Håkon Jacobsen and Tibor Jager
Highly Efficient Key Exchange Protocols with Optimal Tightness
Lecture Notes in Computer Science

Karin Erdmann, Øyvind Solberg and Xingting Wang
On the structure and cohomology ring of connected Hopf algebras
Journal of Algebra

Steffen Oppermann, Chrysostomos Psaroudakis and Torkil Utvik Stai
Change of rings and singularity categories
Advances in Mathematics

Øyvind Solberg, Henning Krause, Aslak Bakke Buan and Nicole Snashall
Support varieties—an axiomatic approach
Mathematische Zeitschrift

View all publications