# 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 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

## Seminars

## Conferences and workshops

- Flash Talks in Representation Theory, January 2021
- Conference for Idun Reiten, May 2017
- GAP Days 2015
- Cluster categories and cluster tilting
- Abelsymposium 2011: Algebras, Quivers and Representations

## Projects

#### Current projects

- Applications of reduction techniques and computations in representation theory (NFR, 2020–2024)
- Secure, Usable and Robust Cryptographic Voting Systems (NFR, 2018–2022)

#### Completed projects

- Representation theory via subcategories (NFR, 2016–2020)
- Clusters, combinatorics and computations in algebra (NFR, 2013–2018)
- Triangulated Categories in Algebra (NFR, 2013–2017)
- Combinatorial and Categorical Methods in Representation Theory (NFR, 2009–2015)

## Graduate courses in algebra

#### Bachelor and master level courses

- MA3201 Rings and Modules
- MA3202 Galois Theory
- MA3203 Ring Theory
- MA3204 Homological Algebra
- TMA4150 Algebra
- TMA4160 Cryptography
- TMA4185 Coding Theory

#### PhD level courses

## Recent publications

Lars Winther Christensen, Sergio Estrada, Li Liang, Peder Thompson, Dejun Wu and Gang Yang

**A refinement of Gorenstein flat dimension via the flat--cotorsion theory**

*Journal of Algebra*

Lars Winther Christensen, Sergio Estrada and Peder Thompson

**The stable category of Gorenstein flat sheaves on a noetherian scheme**

*Proceedings of the American Mathematical Society*

Johanne Haugland

**The Grothendieck Group of an n-exangulated Category**

*Applied Categorical Structures*

Katharine Shultis and Peder Thompson

**Reducibility of parameter ideals in low powers of the maximal ideal**

*Contemporary Mathematics*

Petter Andreas Bergh, Mads Hustad Sandøy and Øyvind Solberg

**On support varieties and tensor products for finite dimensional algebras**

*Journal of Algebra*