# Algebra - 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 studied anonymous communications and payment, which also involved 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.

Members of the algebra group also participates in the **Applied Cryptology Lab (NaCl)**.