Skip to main content
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.

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.




View our seminars:

Lunchtime seminars

Pure mathematics colloquium

Postgraduate pure mathematics seminar

Topology seminar



People, projects, publications and PhDs


Professor Armando Martino


Research interests

  • Geometric Group Theory
  • Actions on Trees and Bass-Serre Theory
  • Automorphisms of Free Groups 

Accepting applications from PhD students

Connect with Armando

Dr Ashot Minasyan

Associate Professor

Research interests

  • Word Hyperbolic
  • Relatively Hyperbolic and Acylindrically Hyperbolic Groups
  • Small Cancellation Theory
Connect with Ashot

Dr Bernhard Koeck


Research interests

  • Riemann-Roch theory
  • (Operations on) Higher Algebraic K-Theory
  • Equivariant Riemann-Roch theory

Accepting applications from PhD students

Connect with Bernhard

Dr Cheuk Yu Mak

Royal Society University Research Fellow

Research interests

  • Symplectic topology
  • Fukaya category
  • Homological mirror symmetry

Accepting applications from PhD students

Connect with Cheuk Yu

Dr Daniel Kasprowski

Senior Research Fellow

Research interests

  • Topology of 4-manifolds
  • Geometric topology
  • Coarse geometry
Connect with Daniel

Professor David Gammack

Associate Dean Education
Connect with David

Professor Graham Niblo FIMA


Research interests

  • Geometric group theory
  • Non-commutative geometry
  • Low dimensional topology

Accepting applications from PhD students

Connect with Graham

Professor Ian Leary

Professor in Pure Mathematics

Research interests

  • Geometric Group Theory
  • Cohomology of Groups
  • Classifying Spaces for Families of Subgroups

Accepting applications from PhD students

Connect with Ian

Professor Jacek Brodzki

Head of School

Research interests

  • Topological data analysis
  • Applications of topology to medicine, biology, chemistry, physics, computer science
  • Noncommutative Geometry

Accepting applications from PhD students

Connect with Jacek

Dr Jan Spakula

Associate Professor

Research interests

  • C*-algebras, noncommutative geometry
  • geometric and analytic group theory
  • coarse geometry

Accepting applications from PhD students

Connect with Jan

Related research institutes, centres and groups