Research interests:

My general research revolves around low-dimensional groups. I am particularly interested in one-relator groups, free-by-cyclic groups and graphs of groups. Within these classes I mainly think about hyperbolicity, coherence, the conjugacy problem and the efficiency of the word problem.

Preprints:

1) The geometry of subgroups of mapping tori of free groups, (arXiv).

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

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

4) Lifting relations in right orderable groups, (arXiv).

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

Publications:

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

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

3) 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.).

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

5) Hyperbolic one-relator groups (arXiv, Published in Canad. J. Math.).

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

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

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.