# Topology

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.

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.

Group home page

## Members

Academic staff | |||||
---|---|---|---|---|---|

Name | Office | Phone | VCard | ||

Prof Tom Bridgeland FRS | J18B | 23747 | T.Bridgeland | vcard | Algebraic geometry and mirror symmetry |

Dr Paul Johnson | J6b | 23775 | Paul.Johnson | vcard | Algebraic Geometry, Combinatorics |

Dr Paul Mitchener | J20 | 23858 | P.Mitchener | vcard | $C^\ast$-categories, Analytic and algebraic $K$-theory, Assembly maps, Coarse Geometry |

Prof Ieke Moerdijk | J13 | 23843 | i.moerdijk@uu.nl | vcard | Algebraic and differential topology, category theory |

Prof Neil Strickland | J26 | 23852 | N.P.Strickland | vcard | Algebraic topology, formal group theory |

Prof Sarah Whitehouse | J6c | 23870 | S.Whitehouse | vcard | Algebraic topology |

Dr Simon Willerton | J19 | 23823 | S.Willerton | vcard | quantum topology, algebraic topology, category theory, metric spaces |

Teaching fellows | |||||
---|---|---|---|---|---|

Name | Office | Phone | VCard | ||

Dr Fionntan Roukema | K09 | 23872 | F.Roukema | vcard | Low dimensional topology, Dehn surgery, knot theory. |

Honorary academic staff | |||||
---|---|---|---|---|---|

Name | Office | Phone | VCard | ||

Dr Eugenia Cheng | E.Cheng | vcard | Category theory | ||

Prof John Greenlees | J.Greenlees | vcard | Equivariant topology, commutative algebra, algebraic topology |

Emeritus professors | |||||
---|---|---|---|---|---|

Name | Office | Phone | VCard | ||

Prof Victor Snaith | V.Snaith | vcard | Algebraic K-theory, algebraic topology, algebraic geometry, representation theory |

Postgraduate students | |||||
---|---|---|---|---|---|

Name | Office | Phone | VCard | ||

Nicola Bellumat | NBellumat1 | vcard | |||

James Brotherston | J25 | JABrotherston1 | vcard | ||

Neil Hansford | J18a | NDHansford1 | vcard | Functional analysis, algebraic topology | |

Mr Joseph Martin | J14a | JMartin13@sheffield.ac.uk | vcard | ||

Luca Pol | J14b | LPol1 | vcard | (Equivariant) stable homotopy theory | |

Miss Eve Pound | J14a | EPound1 | vcard | ||

Jordan Williamson | J14b | JWilliamson3 | vcard | Equivariant stable homotopy theory and model categories | |

Mr Yirui Xiong | J14a | YXiong20@sheffield.ac.uk | vcard |

## Current grants

Rigidity and Hasse-Tate models in algebra, geometry and topology | EPSRC |

## Past grants

Algebraic Rational G-Equivariant Stable Homotopy Theory for Profinite Groups and Extensions of a Torus | EPSRC |

Rational equivariant cohomology theories | EPSRC |