Research interests:

My general research revolves around properties of low-dimensional groups. I mainly think about (relative) hyperbolicity, (relative) quasi-conexity, coherence, the finitely generated intersection property and certain algorithmic problems. I am particularly interested in one-relator groups, free-by-cyclic groups and graphs of groups.

Preprints:

17: Finite complete rewriting systems for graphs of free groups with applications to free-by-cyclic, one-relator, and three-manifold groups, (with Robert D. Gray, arXiv, 2026).

16: Coherent RFRS groups, (Appendix, main article by Sam P. Fisher and Pablo Sánchez-Peralta, arXiv, 2026).

1. The finitely generated intersection property in fundamental groups of graphs of groups, (with Jordi Delgado, Jone Lopez de Gamiz Zearra, Mallika Roy, Pascal Weil, arXiv, 2025).

14: Group pairs, coherence and Farrell–Jones Conjecture for $K_0$, (with Andrei Jaikin-Zapirain, Pablo Sánchez-Peralta, arXiv, 2025).

13: The geometry of subgroups of mapping tori of free groups, (arXiv, 2025).

12: Pullbacks and intersections in categories of graphs of groups, (with Jordi Delgado, Jone Lopez de Gamiz Zearra, Mallika Roy, Pascal Weil, arXiv, 2025).

11: The theory of one-relator groups: history and recent progress, (with Carl-Fredrik Nyberg-Brodda, arXiv, 2025).

10: Lifting relations in right orderable groups, (arXiv, accepted at J. Lond. Math. Soc., 2024).

9: On the intersections of finitely generated subgroups of free groups: reduced rank to full rank (arXiv, 2021).

Publications:

8: Embedding finitely generated free-by-cyclic groups in {finitely generated free}-by-cyclic groups, (arXiv, Published in Int. Math. Res. Not., 2026).

7: Residually rationally solvable one-relator groups, (arXiv, Published in Bull. Lond. Math. Soc., 2025).

6: On the coherence of one-relator groups and their group algebras (with Andrei Jaikin-Zapirain, arXiv, Alexander Engel’s blog, Published in Ann. of Math., 2025).

5: Group rings of three-manifold groups (with Dawid Kielak, arXiv, Published in Proc. Amer. Math. Soc., 2024).

4: Virtually free-by-cyclic groups (with Dawid Kielak, arXiv, Alexander Engel’s blog, Published in Geom. Funct. Anal., 2024).

3: Hyperbolic one-relator groups (arXiv, Published in Canad. J. Math., 2024).

2: One-relator hierarchies (arXiv, Alexander Engel’s blog, Published in Duke Math. J., 2025).

1: The fully compressed subgroup membership problem (arXiv, Published in Journal of Algebra, 2023).

Other work

1) Slides from the minicourse One-relator groups and the coherence property I gave at the KIAS workshop on One RElator groups and other Aspects of GGT can be found here.

2) My PhD thesis can be found here.

3) During my PhD I put together a database of one-relator groups. More information can be found here.