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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.

About

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.

 

Seminars

 

View our seminars:

Lunchtime seminars

Pure mathematics colloquium

Postgraduate pure mathematics seminar

Topology seminar

 

 

People, projects, publications and PhDs

People

Professor Jelena Grbic

Professor of Mathematics

Research interests

  • Topology
  • Algebra
  • Combinatorics

Accepting applications from PhD students

Email: j.grbic@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ

Professor Jim Anderson BA, PhD, PFHEA

Professor of Mathematics

Research interests

  • Hyperbolic space and its isometries
  • Kleinian groups (discrete groups of isometries of hyperbolic 3-space)
  • Signatures of actions of automorphism groups on Riemann surfaces

Accepting applications from PhD students

Email: j.w.anderson@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ

Dr Jim Renshaw PhD

Associate Professor

Research interests

  • Algebraic semigroup theory
  • Actions of semigroups and monoids on sets and ordered structures.
  • Semigroup amalgams and the homological classification theory of monoids.

Accepting applications from PhD students

Email: j.h.renshaw@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ

Dr Kevin Boucher

Research Fellow

Research interests

  • geometric and analytic group theory
  • dynamics and group actions
  • harmonic analysis

Mx Luke Waite

Research interests

  • Fuchsian Groups
  • Tiling the Hyperbolic Plane
  • Geometric Group Theory

Email: l.waite@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ

Dr Nansen Petrosyan

Associate Professor

Accepting applications from PhD students

Email: n.petrosyan@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ

Dr Nick Wright

Associate Professor

Research interests

  • Coarse geometry
  • Non-commutative geometry
  • The Baum-Connes conjecture

Accepting applications from PhD students

Email: n.j.wright@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ

Emeritus Professor Peter Kropholler

Research interests

  • Splittings of groups and group actions on trees. Ends of groups.
  • Groups with Eilenberg–Mac Lane spaces of finite type, their structure and their classifying spaces for proper actions.
  • Modular Invariant Theory.

Accepting applications from PhD students

Email: p.h.kropholler@southampton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ

Dr Ruben Sanchez-Garcia

Professor

Research interests

  • Network modelling and analysis
  • Applied Topology

Accepting applications from PhD students

Email: r.sanchez-garcia@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ

Professor Stephen Theriault

Professor of Mathematics

Research interests

  • The homotopy theory of spheres and Moore spaces.
  • Applications of homotopy theory to Lie groups, gauge groups and manifolds.
  • Polyhedral products and toric topology. 

Accepting applications from PhD students

Email: s.d.theriault@soton.ac.uk

Address: B54, West Highfield Campus, University Road, SO17 1BJ

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