### Geometric group theory

My research is in geometric group theory. It's about using geometry (i.e. drawing pictures) to help us understand groups, which can otherwise be fairly dry algebraic objects (i.e. a bunch of letters on a piece of paper).

To expand on this in a more precise way, I am interested in algebraic and topological aspects of groups and explore many of these ideas using geometry. Common themes for my work involve *rigidity problems* (such as classifying maps between different families of groups or describing automorphism groups of complexes) and the study of *classifying spaces of groups* (such as constructing nice classifying spaces for groups or exploring the (co)homology of these classifying spaces). Much of my work is on automorphism groups of free groups and, more generally, automorphism groups of right-angled Artin groups. Other areas of interest that are touched upon in the papers below are lower-central series and other central filtrations of groups, deformation spaces of trees, subspace arrangements, and asymptotic dimension.

### Preprints

#### Cohen-Macaulay Complexes, Duality Groups, and the dualizing module of \(\mathrm{Out}(F_N) \)

With Thomas Wasserman.arXiv.

#### Duality for Cohen-Macaulay Complexes through Combinatorial Sheaves

With Thomas Wasserman.arXiv.

#### Rigidity of the Torelli subgroup in \(\mathrm{Out}(F_N) \).

With Sebastian Hensel and Camille Horbez.arXiv.

### Accepted

#### Direct products of free groups in \(\mathrm{Aut}(F_N) \).

*To appear in GAFA.*

With Martin Bridson.

arXiv.

#### On the geometry of the free factor graph for \(\mathrm{Aut}(F_N) \).

*To appear in GGD.*

With Mladen Bestvina and Martin Bridson.

arXiv.

### Published Articles

#### Commensurations of \(\mathrm{Aut}(F_N) \) and its Torelli subgroup.

*Geometric and Functional Analysis, 2024.*

With Martin Bridson.

arXiv. Journal.

#### Aut-invariant quasimorphisms on groups.

*Transactions of the AMS, 2023.*

With Francesco Fournier-Facio.

arXiv. Journal.

#### A note on virtual duality and automorphism groups of right-angled Artin groups.

*Glasgow Mathematical Journal, 2023.*

With an appendix by Benjamin Brück.

arXiv. Journal.

#### Calculating the virtual cohomological dimension of the automorphism group of a RAAG.

*Bulletin of the LMS, 2021.*

With Matthew Day and Andrew Sale.

arXiv. Journal.

The algorithm described in this paper was implemented in Python by Yutong Dai and is available here.

#### On the topological dimensions of some hyperbolic \(\mathrm{Out}(F_N) \)-graphs.

*Pacific Journal of Mathematics, 2020.*

With Mladen Bestvina and Camille Horbez.

arXiv. Journal.

#### Commensurations of subgroups of \( \mathrm{Out}(F_N) \).

*Transactions of the AMS, 2020.*

With Camille Horbez.

arXiv. Journal.

#### Relative automorphism groups of right-angled Artin groups.

*Journal of Topology, 2019.*

With Matthew Day.

arXiv. Journal.

#### Subspace arrangements, BNS invariants, and pure symmetric outer automorphisms of right-angled Artin groups.

*Groups, Geometry, and Dynamics, 2018.*

With Matthew Day.

arXiv. Journal.

#### The lower central series of a right-angled Artin group.

*Lâ€™Enseignement MathÃ©matique, 2015.*

arXiv. Journal.

#### Centralisers of Dehn twist automorphisms of free groups.

*Proc. Cambridge Philos. Soc., 2015.*

With Moritz Rodenhausen.

arXiv. Journal.

#### Automorphisms of the graph of cyclic splittings of a free group.

*Geometriae Dedicata, 2015.*

With Camille Horbez.

arXiv. Journal.

#### Folding free group automorphisms.

*Q.J. Math, 2014.*

arXiv. Journal.

#### Johnson homomorphisms and actions of higher-rank lattices on right-angled Artin groups.

*Journal of the LMS, 2013.*

arXiv. Journal.

#### Actions of higher-rank lattices on free groups.

*Compositio Mathematica, 2011.*

With Martin Bridson.

arXiv. Journal.