Type of address | Postal address |
---|---|

Country/Territory | United Kingdom |

The research interests of our group cover a wide range of topics on the interface between algebra and geometry.

Geometric objects can be conveniently encoded using algebra. For example, a circle or ellipse in the plane can be described by a quadratic polynomial equation. Higher degree polynomials give more interesting spaces called "algebraic varieties", which we can study using tools from ring theory, or using more advanced tools like derived categories. The symmetries of a geometric object form a group, which can be studied using pure algebra and representation theory.

Conversely, geometric techniques can often be applied to algebraic objects. For example, you can often deform algebraic objects in families called moduli spaces, which have natural notions of geometry and topology. Or you can deduce something about a group by letting it act on a well-understood metric space.

In our department, the algebra and geometry group conducts research mainly in:

- representation theory of groups and algebras,
- group theory and geometric group theory,
- Lie algebras and algebraic groups,
- homotopical and homological algebra,
- algebraic topology,
- deformation theory,
- noncommutative geometry,
- symplectic topology.

- E-pub ahead of print
## Segre products of cluster algebras

Grabowski, J. & Hindmarch, L., 6/10/2024, (E-pub ahead of print) In: Bulletin of the London Mathematical Society. 10 p.Research output: Contribution to Journal/Magazine › Journal article › peer-review

- Published
## New cluster algebras from old: integrability beyond Zamolodchikov periodicity

Hone , A., Kim, W. & Mase, T., 24/09/2024, In: Journal of Physics A: Mathematical and Theoretical. 57, 41, 415201.Research output: Contribution to Journal/Magazine › Journal article › peer-review

- Published
## Enriched Koszul duality

Eurenius, B., 09/2024, In: Journal of Homotopy and Related Structures. 19, 3, p. 397-429 33 p.Research output: Contribution to Journal/Magazine › Journal article › peer-review

## Homological invariants of Fourier algebras

Activity: Talk or presentation types › Invited talk

## Simple-mindedness, silting and stability

Activity: Participating in or organising an event types › Participation in conference - Academic

## Clusters and their Applications in the North (CLAN)

Activity: Participating in or organising an event types › Participation in conference - Academic