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.

Articles:

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

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

3) Residually rationally solvable one-relator groups, (arXiv).

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

5) On the coherence of one-relator groups and their group algebras (with Andrei Jaikin-Zapirain, arXiv, Alexander Engel’s blog, to appear in Annals of Mathematics).

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

7) Hyperbolic one-relator groups (arXiv, Canad. J. Math.).

8) One-relator hierarchies (arXiv, Alexander Engel’s blog, to appear in Duke Math. J.).

9) The fully compressed subgroup membership problem (arXiv, Journal of Algebra).

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

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.