The work of the Topology group is focused on stable homotopy theory, and equivariant versions for spectra with action of a compact Lie group. One major theme is elliptic cohomology, which has rich connections with the work of the Number Theory group. Another theme involves the commutative algebra of generalised cohomology rings, particularly in an equivariant context, which again interacts strongly with the Algebra group.

A third body of work involves the categorical foundations of homotopy theory, in terms of model categories and their derived categories (which are often triangulated). The group has worked extensively on highly structured ring spectra and their modules, which also fall under this heading.


Academic staff
Name Office Phone Email VCard  
Prof Tom Bridgeland FRS J18B 23747 vcard Algebraic geometry and mirror symmetry
Prof John Greenlees J15 23786 vcard Equivariant topology, commutative algebra, algebraic topology
Dr Nick Gurski J07 23838 vcard Higher dimensional category theory, homotopy theory
Dr Paul Johnson J6b 23775 vcard Algebraic Geometry, Combinatorics
Dr Paul Mitchener J20 23858 vcard $C^\ast$-categories, Analytic and algebraic $K$-theory, Assembly maps, Coarse Geometry
Prof Ieke Moerdijk J13 23843 vcard Algebraic and differential topology, category theory
Prof Neil Strickland J26 23852 vcard Algebraic topology, formal group theory
Prof Sarah Whitehouse J6c 23870 vcard Algebraic topology
Dr Simon Willerton J19 23823 vcard quantum topology, algebraic topology, category theory, metric spaces

Teaching fellows
Name Office Phone Email VCard  
Dr Fionntan Roukema K09 23872 vcard Low dimensional topology, Dehn surgery, knot theory.

Honorary academic staff
Name Office Phone Email VCard  
Dr Eugenia Cheng   vcard Category theory

Emeritus professors
Name Office Phone Email VCard  
Prof Victor Snaith   vcard Algebraic K-theory, algebraic topology, algebraic geometry, representation theory

Postgraduate students
Name Office Phone Email VCard  
Mr Mohammad Al-Boshmki J14a 23879 vcard Algebraic Topology
Dean Barber J25 23767 vcard Algebraic topology and operads
Sarah Browne H10a vcard Non-commutative geometry, Functional Analysis, Topology.
Gemma Halliwell J25 23767 vcard
Neil Hansford J18a vcard Functional analysis, algebraic topology
Samuel Hutchinson J25 23767 vcard Algebraic Topology
Mr Shadman Kareem J25 23767 vcard
Dimitar Kodjabachev J26 vcard (equivariant) (stable) homotopy theory
William Mycroft J25 23767 vcard
Luca Pol   vcard Stable homotopy theory and K-theory
Thomas Sutton J25 23767 vcard
Jordan Williamson   vcard Equivariant stable homotopy theory and model categories

Visiting researchers
Name Office Phone Email VCard  
Dr Constanze Roitzheim   vcard Algebraic topology, stable homotopy theory

Current grants


Past grants