Department of Mathematical Sciences

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.

Contact

Øyvind Solberg. Photo.Professor Øyvind Solberg
Head of the Algebra Group

 

Staff – Algebra Group

Projects

Current Projects

Completed Projects

Recent Publications

Petter Andreas Bergh, Gustavo Jasso and Marius Thaule
Higher n-angulations from local rings
Journal of the London Mathematical Society

Reiner Hermann
Exact sequences, Hochschild cohomology, and the Lie module structure over the M-relative center
Journal of Algebra

View all publications