Preprints

1. Heim, P., MacManus, J., Mineh, L. (2026). Realising all countable groups as quasi-isometry groups. arXiv preprint arXiv:2601.06261. Link
   Abstract

   Given any countable group \(G\), we construct uncountably many quasi-isometry classes of proper geodesic metric spaces with quasi-isometry group isomorphic to \(G\). Moreover, if the group \(G\) is a hyperbolic group, the spaces we construct are hyperbolic metric spaces.

   We make use of a rigidity phenomenon for quasi-isometries exhibited by many symmetric spaces, called strong quasi-isometric rigidity. Our method involves the construction of new examples of strongly quasi-isometrically rigid spaces, arising as graphs of strongly quasi-isometrically rigid rank-one symmetric spaces.

2. MacManus, J. (2025). Vertex-transitive graphs with uniformly bisecting quasi-geodesics. arXiv preprint arXiv:2511.10759. Link
   Abstract

   Suppose that \(X\) is an infinite, connected, locally finite, quasi-transitive graph with the property that every bi-infinite quasi-geodesic uniformly coarsely separates \(X\) into exactly two deep pieces. We show that such an \(X\) is quasi-isometric to either the Euclidean plane or the hyperbolic plane. In particular, if \(X\) is a Cayley graph of a finitely generated group \(G\) with the above property, then \(G\) is a virtual surface group. This can be interpreted as an extension of the well-known fact that a hyperbolic group with circular boundary is virtually Fuchsian.

   Our theorem positively resolves Problem 14.98 of the Kourovka Notebook, posed by V. A. Churkin in 1999. The proof uses an isoperimetric inequality of Varopoulos to show that if such a graph has the above property, then either it is hyperbolic or has quadratic growth.

3. MacManus, J. (2024). A note on transitive graphs quasi-isometric to planar (Cayley) graphs. arXiv preprint arXiv:2407.13375. Link
   Abstract

   Given a connected, locally finite, quasi-transitive graph \(X\) which is quasi-isometric to a planar graph \(\Gamma\), we remark that one can upgrade \(\Gamma\) to be a planar Cayley graph, answering a question raised by Esperet--Giocanti and Hamann.

4. Baligács, J., MacManus, J. (2024). The metric Menger problem. arXiv preprint arXiv:2403.05630. Link
   Abstract

   We study a generalization of the well-known disjoint paths problem which we call the metric Menger problem, denoted \(MM(r,k)\), where one is given two subsets of a graph and must decide whether they can be connected by \(k\) paths of pairwise distance at least \(r\). We prove that this problem is \(NP\)-complete for every \(r\geq 3\) and \(k\geq 2\) by giving a reduction from \(3SAT\). This resolves a conjecture recently stated by Georgakopoulos and Papasoglu.

5. MacManus, J., Mineh, L. (2024). Tiling in some nonpositively curved groups. arXiv preprint arXiv:2401.09545. Link
   Abstract

   We prove that acylindrically hyperbolic groups are monotileable. That is, every finite subset of the group is contained in a finite tile. This provides many new examples of monotileable groups, and progress on the question of whether every countable group is monotileable. In particular, one-relator groups and many Artin groups are monotileable.

6. MacManus, J. (2023). Accessibility, planar graphs, and quasi-isometries. arXiv preprint arXiv:2310.15242. Link
   Abstract

   We prove that a connected, locally finite, quasi-transitive graph which is quasi-isometric to a planar graph is necessarily accessible. This leads to a complete classification of the finitely generated groups which are quasi-isometric to planar graphs. In particular, such a group is virtually a free product of free and surface groups, and thus virtually admits a planar Cayley graph.

Publications

1. MacManus, J. (2025). Fat minors in finitely presented groups. Combinatorica 45 (4), 40 arXiv link
   Abstract

   We show that a finitely presented group virtually admits a planar Cayley graph if and only if it is asymptotically minor-excluded, partially answering a conjecture of Georgakopoulos and Papasoglu in the affirmative.

2. MacManus, J. (2024). Deciding if a hyperbolic group splits over a given quasiconvex subgroup. Groups, Geom. Dyn. arXiv link
   Abstract

   We present an algorithm which decides whether a given quasiconvex residually finite subgroup \(H\) of a hyperbolic group \(G\) is associated with a splitting. The methods developed also provide algorithms for computing the number of filtered ends \(\tilde e(G,H)\) of \(H\) in \(G\) under certain hypotheses, and give a new straightforward algorithm for computing the number of ends \(e(G,H)\) of the Schreier graph of \(H\). Our techniques extend those of Barrett via the use of labelled digraphs, the languages of which encode information on the connectivity of \(\partial G - \Lambda H\).

3. Alexandru, C.-M., Bridgett-Tomkinson, E., Linden, N., MacManus, J., Montanaro, A., Morris, H. (2020). Quantum speedups of some general-purpose numerical optimisation algorithms. Quantum Science and Technology, 5(4), 045014 arXiv link
   Abstract

   We give quantum speedups of several general-purpose numerical optimisation methods for minimising a function \(f : \mathbb{R}^n \to \mathbb{R}\). First, we show that many techniques for global optimisation under a Lipschitz constraint can be accelerated near-quadratically. Second, we show that backtracking line search, an ingredient in quasi-Newton optimisation algorithms, can be accelerated up to quadratically. Third, we show that a component of the Nelder-Mead algorithm can be accelerated by up to a multiplicative factor of \(O(\sqrt{n})\text{.}\) Fourth, we show that a quantum gradient computation algorithm of Gilyén et al can be used to approximately compute gradients in the framework of stochastic gradient descent. In each case, our results are based on applying existing quantum algorithms to accelerate specific components of the classical algorithms, rather than developing new quantum techniques.

Thesis

• Find my PhD thesis, titled Splittings, tiles, and planarity: a trio of problems in geometric group theory, at this link.

Talks

1. North Dakota State Univeristy, Fargo, AMS Sectional Meeting (Upcoming, April 2026) - TBC
2. Isaac Newton Institute, Cambridge, OGG Colloquium (November 2025) - All countable groups are quasi-isometry groups.
3. University of Bristol, Algebra Seminar (October 2025) - On why quasi-isometry groups mean everything to me.
4. University of Oxford, Geometric Group Theory Seminar (May 2025) - Coarse geometry of planar groups.
5. University of Oxford, Junior Topology and Group Theory Seminar (May 2025) - Fat minors and where to find them.
6. Jagiellonian University, Kraków, Theoretical Computer Science Seminar (April 2025) - Asymptotic minors of Cayley graphs.
7. ICMAT, Madrid, Group Theory Seminar (March 2025) - Coarse characterisations of planarity in Cayley graphs.
8. University of Bristol, Geometry and Topology Seminar (October 2024) - Coarse characterisations of planarity in Cayley graphs.
9. World of Geometric Group Theory IV, Online (September 2024) - Coarsely characterising planarity in Cayley graphs.
10. University of Warwick, Geometry and Topology Seminar (February 2024) - Groups quasi-isometric to planar graphs.
11. University of Exeter, ITMAIA (February 2024) - Tilings in groups.
12. University of Oxford, Junior Topology and Group Theory Seminar (October 2023) - Reasons to be accessible.
13. University of Southampton, ECSTASy (August 2023) - Characterising surface groups.
14. Heriot-Watt University, PGTC (July 2023) - Understanding limit sets via finite automata.
15. University of Oxford, Junior Topology and Group Theory Seminar (May 2023) - Planar Cayley graphs and accessibility.
16. University of Cambridge, Junior Geometry Seminar (April 2023) - Splitting detection, and limit set complements.
17. University of Bristol, Junior Geometry Seminar (February 2023) - Will it split? Recognising edge groups in hyperbolic groups.
18. University of Oxford, Junior Topology and Group Theory Seminar (March 2022) - Detecting topological features of the Gromov boundary.

Misc.

• I ran the the Junior Topology and Group Theory seminar at Oxford for 2022-23.