Type of address | Postal address |
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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.

- Published
## An explicit minorant for the amenability constant of the Fourier algebra

Choi, Y., 30/11/2023, In: International Mathematics Research Notices. 2023, 22, p. 19390–19430Research output: Contribution to Journal/Magazine › Journal article › peer-review

- Published
## Modern Trends in Algebra and Representation Theory

Jordan, D. (ed.), Mazza, N. (ed.) & Schroll, S. (ed.), 31/08/2023, Cambridge: Cambridge University Press. 430 p. (London Mathematical Society Lecture Note Series; vol. 486)Research output: Book/Report/Proceedings › Proceedings

- Published
## On the subalgebra lattice of a restricted Lie algebra

Paez-Guillan, P., Siciliano, S. & Towers, D., 1/03/2023, In: Linear Algebra and its Applications. 660, p. 47-65 19 p.Research output: Contribution to Journal/Magazine › Journal article › peer-review

## Coorganisation of the Mini-Workshop at the Mathematisches Forschungsinstitut Oberwolfach entitled Homological Aspects for TDLC-Groups

Activity: Participating in or organising an event types › Other

## Derivations and 2-cocycles on Fourier algebras of connected groups

Activity: Talk or presentation types › Invited talk

## UKRI Talent Peer Review College (External organisation)

Activity: Membership types › Membership of committee