Marco Linton

Research interests

Coherence·compact cores·splittings·L²-invariants·group (co)homology·free groups·one-relator groups·hyperbolic groups·quasi-convex subgroups

Preprints

1. Finite complete rewriting systems for graphs of free groups with applications to free-by-cyclic, one-relator, and three-manifold groups
   with Robert Gray · 2026 · arXiv:2607.07496
2. Coherent RFRS groups
   appendix to an article by Sam P. Fisher and Pablo Sánchez-Peralta · 2026 · arXiv:2603.16763
3. The finitely generated intersection property in fundamental groups of graphs of groups
   with Jordi Delgado, Jone Lopez de Gamiz Zearra, Mallika Roy, Pascal Weil · 2025 · arXiv:2512.12635
4. Group pairs, coherence and Farrell–Jones Conjecture for K₀
   with Andrei Jaikin-Zapirain, Pablo Sánchez-Peralta · 2025 · arXiv:2510.23518
5. The geometry of subgroups of mapping tori of free groups
   2025 · arXiv:2510.03145
6. Pullbacks and intersections in categories of graphs of groups
   with Jordi Delgado, Jone Lopez de Gamiz Zearra, Mallika Roy, Pascal Weil · 2025 · arXiv:2508.04362
7. The theory of one-relator groups: history and recent progress
   with Carl-Fredrik Nyberg-Brodda (2025) · to appear as chapter in Recent Progress in Mathematics, KIAS Springer Ser. Math. · arXiv:2501.18306
8. On the intersections of finitely generated subgroups of free groups: reduced rank to full rank
   2021 · arXiv:2108.10814

Publications

9. Lifting relations in right orderable groups
   accepted, J. Lond. Math. Soc. (2026) · arXiv:2412.17057
10. Embedding finitely generated free-by-cyclic groups in {finitely generated free}-by-cyclic groups
    Int. Math. Res. Not. 2026 (2026), no. 4 · arXiv:2510.10178
11. Residually rationally solvable one-relator groups
    Bull. Lond. Math. Soc. 58 (2025), no. 1 · arXiv:2407.09272
12. On the coherence of one-relator groups and their group algebras
    with Andrei Jaikin-Zapirain · Ann. of Math. (2) 201 (2025), no. 3, 909–959 · arXiv:2303.05976
13. Group rings of three-manifold groups
    with Dawid Kielak · Proc. Amer. Math. Soc. 152 (2024), no. 5, 1939–1946 · arXiv:2303.15907
14. Virtually free-by-cyclic groups
    with Dawid Kielak · Geom. Funct. Anal. 34 (2024), no. 5, 1580–1608 · arXiv:2302.11500
15. Hyperbolic one-relator groups
    Canad. J. Math. 78 (2026), no. 1, 35–61 · arXiv:2211.04371
16. One-relator hierarchies
    Duke Math. J. 174 (2025), no. 4, 747–802 · arXiv:2202.11324
17. The fully compressed subgroup membership problem
    J. Algebra 628 (2023), 562–583 · arXiv:2110.10055

Selected invited talks

Teaching and supervision

In 2025 I taught the advanced algebra course on Geometric Group Theory at the Universidad Autónoma de Madrid. Between 2018 and 2022 I was a teaching assistant at the University of Warwick, across Discrete Mathematics, Algebra II, Geometry, Introduction to Topology and Algebraic Topology.

I have supervised Alba González González (MSc, Universidad Autónoma de Madrid, now a PhD student at Oxford) and Miguel Ángel Royo Miguel (JAE summer research student, Universidad de Zaragoza).

Minicourses

Other work

I am currently organising YGGT 2027 at the ICMAT together with Macarena Arenas, Sam Fisher, Alejandra Garrido, Claudio Llosa-Isenrich and Rachel Skipper.

Slides from my minicourse One-relator groups and the coherence property, given at the KIAS workshop on One-Relator groups and other Aspects of GGT, are available here.

My PhD thesis, One-relator hierarchies, can be found here.

During my PhD I also put together a database of one-relator groups.

Contact

Some pictures