Course material for my Part III Profinite Groups course may be found here.

Research interests

My work mostly centres around interactions of the worlds of geometric group theory and geometric topology with profinite groups. This involves both the study of residual properties and profinite completions of groups and the extension of geometric concepts to the category of profinite or pro-p groups.


  1. On the structure of vertex cuts separating the ends of a graph. Pacific J. Math. (Volume 278 Issue 2, Dec 2015).
  2. Profinite properties of RAAGs and special groups. Joint with Robert Kropholler. Bull. Lond. Math. Soc. (Volume 48 Issue 6, Sept 2016).
  3. Profinite rigidity for Seifert fibre spaces. Geom. Dedicata (Volume 188 Issue 1, June 2017).
  4. Virtual pro-p properties of 3-manifold groups. J. Group Theory (Volume 20 Issue 5, Sept 2017).
  5. Profinite rigidity of graph manifolds and JSJ decompositions of 3-manifolds. J. Algebra (Volume 502, May 2018).
  6. Profinite completions, cohomology and JSJ decompositions of compact 3-manifolds. New Zealand J. Math. (Volume 48, 2018).
  7. Relative cohomology theory for profinite groups. J. Pure and Appl. Algebra (Volume 223 Issue 4, April 2019).
  8. On accessibility for pro-p groups. J. Algebra (Volume 525, May 2019).
  9. Profinite rigidity of graph manifolds, II: knots and mapping classes. Israel J. Math. (Volume 233 Issue 1, August 2019).
  10. A criterion for residual p-finiteness of arbitrary graphs of finite p-groups. J. Group Theory (Volume 22 Issue 4, September 2019).
  11. Classification of pro-p PD2 pairs and the pro-p curve complex. Groups Geom. Dyn. (accepted).


  1. Virtually abelian quotients of random groups. Preprint Feb 2019.
  2. Distinguishing crystallographic groups by their finite quotients. Joint with Pawel Piwek and David Popovic. Preprint Oct 2019.
  3. L2 Betti numbers and coherence of random groups. Joint with Dawid Kielak and Robert Kropholler. Preprint Mar 2020.
  4. A sufficient condition for accessibility of pro-p groups. Preprint July 2020.

My doctoral thesis

Profinite Properties of 3-Manifold Groups, Oxford 2018