# Research

My main research field is Geometric Group Theory and consequences of non-positive behaviour in group theory. Classes of groups that I think about often are CAT(0) groups, Morse local-to-global groups, and hierarchically hyperbolic groups, and many other classes of groups with aspects of negative curvature.

I study the effects of negative curvature on aspects such as algebraic, geometric, algorithmic and dynamical properties of groups. Currently, I am expanding my interests and working on the links between negative curvature and other areas of mathematics, such as logic, functional analysis and homological algebra.

#### New preprints

With Murray Elder, Giles Gardam, Adam Piggott, and Kane Townsend: Graphs and groups with unique geodesics. arXiv2311.03730.

With L. Mineh: Separability in Morse local-to-global groups. arXiv2308.11603.

#### Papers

With C. R. Abbott and T. Ng : Hierarchically hyperbolic groups and uniform exponential growth. arXiv1909.00439. Accepted in **Mathematische Zeitschrift**.

With M. Hagen, J. Russell, and A. Sisto: Equivariant hierarchically hyperbolic structures for 3-manifold groups via quasimorphisms. arXiv2206.12244. Accepted in **Annales de l'Institut Fourier**.

With Y. Krifka: A note on subgroups of the Loch Ness monster surface's mapping class group. arXiv2201.10378. Accepted in **Proceedings of the Beyond Hyperbolicity Conference**.

With M. Cordes, J. Russell and A. Zalloum:
Regularity of Morse geodesics and growth of stable subgroups. arXiv2008.06379. Accepted in **Journal of Topology**.

With H. Petyt: Unbounded domains in hierarchically hyperbolic groups. arXiv2007.12535. Accepted in **Groups, Geometry and Dynamics**.

With J. Russell and H. C. Tran: The local to global property for Morse quasi-geodesics. arXiv1908.11292. Accepted in **Mathematische Zeitschrift**.

With J. Russell and H. C. Tran: Convexity in hierarchically hyperbolic spaces. arXiv:1809.09303. Accepted in **Algebraic and Geometric Topology**.

With R. Kropholler: Closure Properties in the Class of Multiple Context Free Groups. arXiv1709.02478. Accepted in **Groups Complexity Cryptology**.

#### Surveys

Introduction to hyperbolic groups. Published version. **Advances in Group Theory and Applications**.

#### Preprints

With H. Petyt and A. Zalloum: Hyperbolic models for CAT(0) spaces. arXiv2207.14127.

With S. Hughes and P. Nairne: Regularity of quasigeodesics characterises hyperbolicity. arXiv2205.08573.

With B. Robbio: Hierarchical hyperbolicity of hyperbolic-2-decomposable groups. arXiv2007.13383.

Hyperbolic HHS II: Graphs of hierarchically hyperbolic groups. arXiv:1801.01850.

Hyperbolic HHS I: Factor Systems and Quasi-convex subgroups. arXiv:1711.10931.

### Minicourses

Groups and Algebras in Bicocca for Young algebrist (GABY): Introduction to hyperbolic groups.

Geometric Group Theory * without* boundaries (20-31 July 2020): Introduction to hierarchically hyperbolic groups.

### Recordings

A talk given in NCNGT: background and research.

Minicourse on hierarchically hyperbolic groups given in Geometric Group Theory * without* boundaries: Part 1, Part 2, Part 3.

### Research talks

University of Vienna; Geometry and Analysis on Groups Research Seminar; (21 Nov 2023): Uniquely geodesic groups are virtually free.

University of Torino; Differential Geometry Seminar; (14 Nov 2023): From graph properties to group theory.

Erwin Schrödinger International Institute for Mathematics and Physics; GAGTA (18 July 2023): Hyperbolic models for CAT(0) spaces.

Stevens Institute of Technology; Groups and Computations (14 June 2023): On a quesiton of Shapiro.

University of Toledo - Virtual; (1 March 2023): Hyperbolic models for CAT(0) spaces .

University of Luxemburg; Geometry and Topology seminar (21 Februrary 2023): Hyperbolic models for CAT(0) spaces.

University of Bristol; Geometry and Topology seminar (31 January 2023): Hyperbolic models for CAT(0) spaces.

University of Warwick; Geometry and Topology seminar (26 January 2023): Combinatorial criteria for hyperbolicity.

University of Heidelberg; DSG seminar (12 Jan 2023): Hyperbolic models for CAT(0) spaces.

Virtual; Nearly Carbon Neutral Geometric Topology conference (NCNGT) (18-25 September 2022): Introductory talk + hyperbolic models for CAT(0) spaces.

Oberwolfach; Topologie (27 July 2022): Hyperbolic models for CAT(0) spaces.

FernUniversität in Hagen; Probabilistic and Geometric Group Theory seminar (26 March 2022): Hyperbolic spaces for CAT(0) groups.

Heriot-Watt; MAXIMALS (23 February 2022): Hyperbolic spaces for CAT(0) groups.

Universtiy of Warwick; Geometry and Topology seminar (27 January 2022): Hyperbolic spaces for CAT(0) groups.

KIT; Weihnachtsworkshop on Geometry and Number Theory 2021 (15-17 December 2021): Detecting hyperbolicity in CAT(0) spaces: from cube complexes to rank rigidity.

University Milano Bicocca; Seminar Al@Bicocca (10 December 2021): Detecting hyperbolicity in CAT(0) spaces: from cube complexes to rank rigidity.

Univesrity of Oxford; Junior Topology and Group Theory seminar (24 November 2021): Embedding subgroups into big mapping class groups.

Queens University; Dynamics, Geometry and Groups Seminar (17 November 2021): Generalizing hyperbolicity via local-to-global behaviour.

University of Oxford; Topology seminar (1 February 2021): Introduction to Hierarchically Hyperbolic Groups.

University of Oxford; Junior Topology and Group Theory seminar (2 December 2020): Generalizing Hyperbolicity via Local-to-Global behaviour.

Heriot-Watt University; MAXIMALS (18 November 2020): Generalizing Hyperbolicity via Local-to-Global behaviour.

CUNY; CUNY Geometry and Topology Seminar (20 October 2020): Quasi-isometric invariance of Hierarchically Hyperbolic Groups.

ETH Zurich; Geometry Seminar (4 March 2020): Generalizing hyperbolicity via local-to-global behavior.

University of Vienna; Geometry and Analysis on Groups Research Seminar (10 December 2019): The local-to-global property for Morse quasi-geodesics.

University of Bristol; Algebra and Geometry Seminar (4 December 2019): The local-to-global property for Morse quasi-geodesics.

University of Oxford; Junior Topology and Group Theory Seminar (26 November 2019): The local-to-global property for Morse quasi-geodesics.

Temple University; Geometry and Topology Seminar (13 March 2019): Local-to-global Morse properties, convexity and hierarchically hyperbolic spaces.

CUNY; CUNY Geometry and Topology Seminar (12 March 2019): Local-to-global Morse properties, convexity and hierarchically hyperbolic spaces.

Tufts; GGTT Seminar (26 February 2019): Local-to-global Morse properties, convexity and hierarchically hyperbolic spaces.

University of Newcastle; Zero-Dimensional Symmetry Seminar (11 December 2018): Convexity and generalizations of hyperbolicity.

University of the Basque Country; Algebra Seminar (8 October 2018): Quasiconvexity in hierarchically hyperbolic spaces.

Korea Institute for Advanced Study; GAGTA 2018 (16 Jul 2018): Non-trivial hierarchical structures on hyperbolic groups.

University of Oxford; Junior Topology and Group Theory Seminar (10 May 2018): Morse subsets of hierarchically hyperbolic spaces.

University of Sheffield; Postgraduate Pure Maths Seminar (9 May 2018): What is geometric group theory (and why people care about it)?.

Univesrity of Warwick; Junior Geometry and Topology Seminar (8 May 2018): Morse subsets in hierarchically hyperbolic spaces.

University of Bielefeld; Homological and Topological methods in Group Theory: Morse subgroups of hierarchically hyperbolic groups.

University of Pisa; Seminario Baby Geometri (22 Jan 2018): Gromov Iperbolicità e generalizzazioni.

### Miscellaneous talks

ETH Zurich; Zurich Graduate Colloquium (25 Feb 2020): What are... the ends of a group.

ETH Zurich; Geometry Graduate Colloquium (31 Oct 2019): An overview of classical Geometric Group Theory.

ETH Zurich; Zurich Graduate Colloquium (25 Sep 2018): What is... A formal language.

ETH Zurich; Geometry Graduate Colloquium (22 Mar 2018): Introduction to hierarchically hyperbolic groups and spaces.

University of Torino; Welcome Home (21 Dec 2017): Introduzione alla teoria geometrica dei gruppi.

ETH Zurich; Informal geometry seminar (15 Nov 2017): Hyperbolically embedded subgroups.

ETH Zurich; Graduate seminar (28 Nov 2017): What is.... a hyperbolic space?

University of Torino: Graduate seminar (19 Apr 2017): Come si disegna un gruppo?