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Research group

Pure Mathematics

Lattice sculpture with fractal patterns

We work with researchers around the world to contribute to research in algebra, analysis, geometry and topology.


We're a team of 30 academics and postgraduate students, and our global network includes groups in the UK, the EU, North America and East Asia. 

We are internationally recognised as research leaders in several fields, including geometric group theory, non-commutative geometry and analysis, algebraic topology and applied topology. 

The Centre for Geometry, Topology, and Applications has created a focal point for a large part of this activity. We run multiple seminars and a colloquium in order to share our latest research results and hear of new research by external speakers. 

Our research can be broadly divided into several categories: 

  • geometric group theory 
  • topology 
  • non-commutative geometry 
  • topological data analysis 
  • semigroup theory 
  • algebraic geometry 

We welcome applications for PhD study in one of our areas of expertise. Please have a look at our research areas and projects, and do not hesitate to contact our staff for more information. 

Research highlights

Projects and publications

Research projects

Our people

The main themes that have appeared in my research in recent years are: classifying spaces for families of subgroups; finiteness condition for groups and connections with algebraic K-theory; spaces satisfying non-positive curvature conditions such as CAT(0)-spaces; special classes of groups such as Artin groups, Coxeter groups and Bestvina-Brady groups.
Professor in Pure Mathematics
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