# Research

My main research field is Geometric Group Theory and consequences of non-positive behaviour in group theory. Two classes of groups that I think about often are hierarchically hyperbolic groups and Morse local-to-global groups.

#### New preprints

With M. Cordes, J. Russell and A. Zalloum: Regularity of Morse geodesics and growth of stable subgroups. Pdf.

With H. Petyt: Unbounded domains in hierarchically hyperbolic groups. arXiv2007.12535.

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

#### Papers

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

#### Preprints

With C. R. Abbott and T. Ng : Hierarchically hyperbolic groups and uniform exponential growth. arXiv1909.00439.

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

With J. Russell and H. C. Tran: Convexity in hierarchically hyperbolic spaces. arXiv:1809.09303.

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

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

### Minicourses

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

### Research talks

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?