Since October 2018 I have been a PhD student at the University of Southampton under the supervision of Professor Ian Leary. Before I became a student at Southampton, I completed an MMath degree at the University of South Wales. In October 2021 I will be joining Dr Dawid Kielak's team in the Mathematical Institute at the University of Oxford

My research is primarily in geometric group theory, often with a topological flavour. More specifically, I am interested in lattices in locally compact groups, cohomology of arithmetic groups, \(L^2\)-invariants, and \(K\)-theory in relation to the isomorphism conjectures.

My recent activities can be found here.

I was one of the organisers of the interdisciplinary seminar series Maths and Mingle. You can read more about Maths and Mingle in our article in the May 2020 edition of the LMS newsletter. I am also co-organising the conference Postgraduate Group Theory 2020 (PGTC 2020).

- Graphs and complexes of lattices,Poster, slides.
*in preparation*.In preparation. - (With Indira L. Chatterji and Peter H. Kropholler) Groups acting on trees and the first \(\ell^2\)-Betti number,arXiv, pdf.
*submitted*.We generalise results of Thomas, Allcock, Thom-Petersen, and Kar-Niblo to the first \(\ell^2\)-Betti number of quotients of certain groups acting on trees by subgroups with free actions on the edge sets of the graphs. - On the equivariant \(K\)- and \(KO\)-homology of some special linear groups, to appear inarXiv, pdf, slides.
*Algebraic and Geometric Topology*.We compute the equivariant \(KO\)-homology of the classifying space for proper actions of \(\textrm{SL}_3(\mathbb{Z})\) and \(\textrm{GL}_3(\mathbb{Z})\). We also compute the Bredon homology and equivariant \(K\)-homology of the classifying spaces for proper actions of \(\textrm{PSL}_2(\mathbb{Z}[\frac{1}{p}])\) and \(\textrm{SL}_2(\mathbb{Z}[\frac{1}{p}])\) for each prime \(p\). Finally, we prove the Unstable Gromov-Lawson-Rosenberg Conjecture for a large class of groups whose maximal finite subgroups are odd order and have periodic cohomology. - Cohomology of Fuchsian groups and non-Euclidean crystallographic groups,arXiv, pdf.
*submitted*.For each geometrically finite non-Euclidean crystallographic group (NEC group), we compute the cohomology groups. In the case where the group is a Fuchsian group, we also determine the ring structure of the cohomology. Finally, we compute the \(L^2\)-Betti numbers of the NEC groups. - (With Nick Gill) The character table of a sharply \(5\)-transitive subgroup of the alternating group of degree \(12\), to appear inJournal, arXiv, pdf.
*International Journal of Group Theory.*In this paper we calculate the character table of a sharply \(5\)-transitive subgroup of \({\rm Alt}(12)\), and of a sharply \(4\)-transitive subgroup of \( \rm{Alt}(11\)). Our presentation of these calculations is new because we make no reference to the sporadic simple Mathieu groups, and instead deduce the desired character tables using only the existence of the stated multiply transitive permutation representations.

- April 2021,
*The Unstable Gromov-Lawson-Rosenberg Conjecture*, Southampton Topology Seminar. - March 2021,
*Lattices in non-positive curvature*, ETH Zurich Geometry graduate colloquium. - March 2021,
*Isometry groups of \(\textrm{CAT}(0)\) spaces*, Southampton PGR Seminar (online edition). - February 2021,
*Lattices in non-positive curvature*, Junior London Algebra Colloquium. - December 2020,
*Spotting infinite groups*, Southampton Lunchtime Seminar. - November 2020,
*The unstable Gromov-Lawson-Rosenberg conjecture for certain \(S\)-arithmetic groups*, New Directions in Group Theory and Triangulated Categories. - August 2020,
*The grandest induction*, Southampton PGR Seminar (online edition). - July 2020,
*On the unstable Gromov-Lawson-Rosenberg conjecture*, Graduate Online Anything Topology Series #3. - November 2019,
*Cohomology of NEC groups*, Southampton Lunchtime Seminar. - October 2019,
*Lattices, trees and symmetric spaces*, USW Mathematical Sciences Seminars. - October 2019,
*Vector bundles and \(K\)-theory*, Southampton Tuesday Evening Seminar. - July 2019,
*The cohomology of cocompact Fuchsian groups*, Postgraduate Group Theory Conference 2019. - May 2019,
*Fuchsian groups and the geometry of surfaces*, Bristol Junior Geometry Seminar. - February 2019,
*Some non-Hopfian groups and their geometries*, Southampton PGR Seminar. - May 2018,
*The character table of a sharply \(5\)-transitive subgroup of \({\rm Alt}(12)\)*, Gregynog 2018.

My institutional page is here.

ResearchGate. Scholar.