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.

Contact

Contact

Øyvind Solberg. Photo.Professor Øyvind Solberg, head of the algebra group.

 

Seminars

Conferences and workshops

Projects

Recent publications

Recent publications

Petter Andreas Bergh, Mads Hustad Sandøy and Øyvind Solberg
On support varieties and tensor products for finite dimensional algebras
Journal of Algebra

Colin Alexander Boyd, Gareth Thomas Davies, Kristian Gjøsteen and Yao Jiang
Fast and Secure Updatable Encryption
Lecture Notes in Computer Science (LNCS)

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

Gareth Thomas Davies, Herman Galteland, Kristian Gjøsteen and Yao Jiang
Cloud-assisted Asynchronous Key Transport with Post-Quantum Security
Lecture Notes in Computer Science (LNCS)

Roman Langrehr and Jiaxin Pan
Tightly Secure Hierarchical Identity-Based Encryption
Journal of Cryptology

Tsutomu Nakamura and Peder Thompson
Minimal semi-flat-cotorsion replacements and cosupport
Journal of Algebra

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