Research

Special groups with an elementary hierarchy are virtually free-by-Z. With Dani Wise. Groups, Geometry, and Dynamics 4:3, 597-603, 2010.

Weak hyperbolicity of cube complexes and quasi-arboreal groups. J. Topol. 7:2, 385-418, 2014.

On embedding CAT(0) cube complexes into products of trees via colouring their hyperplanes. With Victor Chepoi. J. Comb. Theor. Ser. B 103:4, 428-467, 2013.

The simplicial boundary of a CAT(0) cube complex. Alg. Geom. Topol. 13:3, 1299-1367, 2013.

Corrigendum on Theorem 3.10 in the infinite-dimensional case; finite-dimensional case is unaffected (journal version).

Cocompactly cubulated crystallographic groups. J. Lond. Math. Soc. 90 (1): 140-166, 2014.

Cubulated groups: thickness, relative hyperbolicity, and simplicial boundaries. With Jason Behrstock. Groups, Geometry, and Dynamics. (10:2) 649-707, 2016.

Terminology clarification: the word "quasiconvex" is used in two ways in the paper, sometimes confusingly. In arguments not about group actions, it means "any two points in the subspace are joined by a quasigeodesic in the subspace". For a subgroup H of a group G acting geometrically on a cube complex X, "quasiconvex" is intended in the stronger, cubical sense: H-orbits are Hausdorff close to their convex hull in X. Nowadays, one would say "cubically convex-cocompact".

Cocompactly cubulated graph manifolds. With Piotr Przytycki. Isr. J. Math. 207 (1): 377-394, 2015.

Erratum correcting the proof of Lemma 4.7(2) (journal version).

Cubulating hyperbolic free-by-cyclic groups: the irreducible case. With Dani Wise. Duke Math. Jour. (165:9) 1753-1813, 2016.

Thickness, relative hyperbolicity, and randomness in Coxeter groups. With Jason Behrstock and Alessandro Sisto, appendix with Pierre-Emmanuel Caprace. Alg. Geom. Topol. (17:2) 705-740, 2016.

Software associated with the above paper.

Residual finiteness growths of virtually special groups. With Khalid Bou-Rabee and Priyam Patel. Math. Zeit. 279 (1-2): 297-310, 2015.

Cubulating hyperbolic free-by-cyclic groups: the general case. With Dani Wise. Geom. Funct. Anal. 25:1, 134-179, 2015.

Hierarchically hyperbolic spaces I: curve complexes for cubical groups. With Jason Behrstock and Alessandro Sisto. Geom. Topol. (21:3) 1731-1804, 2017.

Quantifying separability in virtually special groups. With Priyam Patel. Pacific Jour. Math. (284:1) 103-120, 2016.

This is a slightly different proof of Theorem A. The main idea is the same, but the argument is modified in a way that avoids some technicalities. Not for publication, just a record for possible later use.

Global structural properties of random graphs. With Jason Behrstock, Victor Falgas-Ravry, and Tim Susse. Int. Math. Res. Not. 2018:5, 1411-1441, 2018.

Source code and data alluded to in the above paper.

Hierarchically hyperbolic spaces II: Combination theorems and the distance formula. With Jason Behrstock and Alessandro Sisto. Pacific J. Math. (299:2) 257-338, 2019.

Asymptotic dimension and small-cancellation for hierarchically hyperbolic spaces and groups. With Jason Behrstock and Alessandro Sisto. Proc. Lond. Math. Soc. (114:5) 890-926, 2017.

Acylindrical hyperbolicity of cubical small-cancellation groups. With Goulnara Arzhantseva. Alg. Geom. Topol. To appear, 2021.

Boundaries and automorphisms of hierarchically hyperbolic spaces. With Matthew Durham and Alessandro Sisto. Geom. Topol. (21:6) 3659-3758, 2017.

Corrigendum fixing an error affecting the proofs of Theorem 7.1 and Theorem 9.15 (journal version).

Some point-set topology comments, mainly explaining why the boundary of a proper HHS is metrisable. Not for publication since it's just giving details of ideas in the paper, but possibly helpful to someone reading Sections 2 and 3.

Cubulating mapping tori of polynomial growth free group automorphisms. With Dani Wise. Preprint, 2016.

	The papers can also be found on the ArXiv in most cases.
	Book/conference proceedings Beyond Hyperbolicity. Co-edited with Richard Webb and Henry Wilton.
	Recent papers On hierarchical hyperbolicity of cubical groups. With Tim Susse. Isr. J. Math. 236, 45-89, 2020. Quasiflats in hierarchically hyperbolic spaces. With Jason Behrstock and Alessandro Sisto. Duke Math. Jour. To appear, 2020. Panel collapse and its applications. With Nicholas Touikan. Groups, Geometry, and Dynamics. 13:4, 1285-1334, 2019. Dehn filling Dehn twists. With François Dahmani and Alessandro Sisto. Proc. A. Royal Soc. Edinburgh. To appear, 2020. A remark on thickness of free-by-cyclic groups. Illinois J. Math. 63:4, 633-643, 2019. Projection complexes and quasimedian maps. With Harry Petyt. Alg. Geom. Topol. To appear, 2021. Deforming cubulations of hyperbolic groups. With Elia Fioravanti. J. Topol. To appear, 2021. A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups. With Jason Behrstock, Alexandre Martin, and Alessandro Sisto. Preprint, 2020. Large facing tuples and a strengthened sector lemma. Tunisian Jour. Math. To appear, 2021. Non-colourable hierarchically hyperbolic groups. Preprint, 2021. Extra-large type Artin groups are hierarchically hyperbolic. With Alexandre Martin and Alessandro Sisto. Preprint, 2021. Real cubings and asymptotic cones of hierarchically hyperbolic groups. With Montserrat Casals-Ruiz and Ilya Kazachkov. Working draft, 2022.
	Older papers Special groups with an elementary hierarchy are virtually free-by-Z. With Dani Wise. Groups, Geometry, and Dynamics 4:3, 597-603, 2010. Weak hyperbolicity of cube complexes and quasi-arboreal groups. J. Topol. 7:2, 385-418, 2014. On embedding CAT(0) cube complexes into products of trees via colouring their hyperplanes. With Victor Chepoi. J. Comb. Theor. Ser. B 103:4, 428-467, 2013. The simplicial boundary of a CAT(0) cube complex. Alg. Geom. Topol. 13:3, 1299-1367, 2013. Corrigendum on Theorem 3.10 in the infinite-dimensional case; finite-dimensional case is unaffected (journal version). Cocompactly cubulated crystallographic groups. J. Lond. Math. Soc. 90 (1): 140-166, 2014. Cubulated groups: thickness, relative hyperbolicity, and simplicial boundaries. With Jason Behrstock. Groups, Geometry, and Dynamics. (10:2) 649-707, 2016. Terminology clarification: the word "quasiconvex" is used in two ways in the paper, sometimes confusingly. In arguments not about group actions, it means "any two points in the subspace are joined by a quasigeodesic in the subspace". For a subgroup H of a group G acting geometrically on a cube complex X, "quasiconvex" is intended in the stronger, cubical sense: H-orbits are Hausdorff close to their convex hull in X. Nowadays, one would say "cubically convex-cocompact". Cocompactly cubulated graph manifolds. With Piotr Przytycki. Isr. J. Math. 207 (1): 377-394, 2015. Erratum correcting the proof of Lemma 4.7(2) (journal version). Cubulating hyperbolic free-by-cyclic groups: the irreducible case. With Dani Wise. Duke Math. Jour. (165:9) 1753-1813, 2016. Thickness, relative hyperbolicity, and randomness in Coxeter groups. With Jason Behrstock and Alessandro Sisto, appendix with Pierre-Emmanuel Caprace. Alg. Geom. Topol. (17:2) 705-740, 2016. Software associated with the above paper. Residual finiteness growths of virtually special groups. With Khalid Bou-Rabee and Priyam Patel. Math. Zeit. 279 (1-2): 297-310, 2015. Cubulating hyperbolic free-by-cyclic groups: the general case. With Dani Wise. Geom. Funct. Anal. 25:1, 134-179, 2015. Hierarchically hyperbolic spaces I: curve complexes for cubical groups. With Jason Behrstock and Alessandro Sisto. Geom. Topol. (21:3) 1731-1804, 2017. Quantifying separability in virtually special groups. With Priyam Patel. Pacific Jour. Math. (284:1) 103-120, 2016. This is a slightly different proof of Theorem A. The main idea is the same, but the argument is modified in a way that avoids some technicalities. Not for publication, just a record for possible later use. Global structural properties of random graphs. With Jason Behrstock, Victor Falgas-Ravry, and Tim Susse. Int. Math. Res. Not. 2018:5, 1411-1441, 2018. Source code and data alluded to in the above paper. Hierarchically hyperbolic spaces II: Combination theorems and the distance formula. With Jason Behrstock and Alessandro Sisto. Pacific J. Math. (299:2) 257-338, 2019. Asymptotic dimension and small-cancellation for hierarchically hyperbolic spaces and groups. With Jason Behrstock and Alessandro Sisto. Proc. Lond. Math. Soc. (114:5) 890-926, 2017. Acylindrical hyperbolicity of cubical small-cancellation groups. With Goulnara Arzhantseva. Alg. Geom. Topol. To appear, 2021. Boundaries and automorphisms of hierarchically hyperbolic spaces. With Matthew Durham and Alessandro Sisto. Geom. Topol. (21:6) 3659-3758, 2017. Corrigendum fixing an error affecting the proofs of Theorem 7.1 and Theorem 9.15 (journal version). Some point-set topology comments, mainly explaining why the boundary of a proper HHS is metrisable. Not for publication since it's just giving details of ideas in the paper, but possibly helpful to someone reading Sections 2 and 3. Cubulating mapping tori of polynomial growth free group automorphisms. With Dani Wise. Preprint, 2016.