Information about
Geometry and Topology
Research activity in Geometry and Topology occurs in several areas, including that of Category Theory.
Our interests in Geometry cover a broad range of topics including: algebraic geometry; differential geometry; geometric group theory; and interactions with differential equations, representation theory and string theory.
Our interests in Topology encompass low-dimensional topology and
algebraic topology. While the study of these subjects often involves
geometric intuition, Topologists tend to study much less `rigid' geometric situations than Geometers.
Category theory looks at mathematics on a large scale. The aim is to strip away inessential details in order to get to the essence of things.
| Academic Staff | Research Interests |
|---|---|
| Hopf algebras and formal groups Stable homotopy theory Structured ring spectra and derived algebraic geometry | |
Algebraic geometry and derived categories | |
|
Recursion and self-similarity | |
Low-dimensional topology | |
Algebraic geometry and derived categories Matrix factorisations and string theory | |
Stable homotopy theory Model categories | |
| Higher category theory | |
Algebraic topology |
In addition, several members of other research groups have interests in Geometry and Topology; specifically:
- Christopher Athorne (Lie symmetry theory with differential Galois theory)
- Tara Brendle (Geometric group theory)
- Kenneth A. Brown (Poisson and algebraic geometry)
Mikhail Feigin (Frobenius manifolds, geometry of hyperplane arrangements)
Peter Kropholler (Geometric group theory)
Steve Pride (low dimensional topology in group representations)