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.
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.
Graduate courses in algebra
|MA3201 Rings and Modules|
|MA3202 Galois Theory|
|MA3203 Ring Theory|
|MA3204 Homological Algebra|
|TMA4185 Coding Theory|
|MA8202 Commutative Algebra|
|MA8203 Algebraic Geometry|
|MA8205 Representation Theory of Algebras|
|MA8206 Advanced Cryptography|