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.

Papers

  1. With H. Petyt and A. Zalloum: Stable cylinders and fine structures for hyperbolic groups and curve graphs. Pdf.
  2. With S. Hughes and P. Nairne: Regularity of quasigeodesics characterises hyperbolicity. arXiv2205.08573. Accepted in Proc. R. Soc. Edinb. A: Math.
  3. With V. He and S. Zbinden: Sigma-compactness of Morse boundaries in Morse local-to-global groups and applications to stationary measures. arXiv2407.18863.
  4. With C. Drutu and S. Zbinden: Combing, local-to-global properties for Morse quasi-geodesics and divergence. Pdf.
  5. With L. Mineh: Separability in Morse local-to-global groups. arXiv2308.11603. Accepted in Bull. London Math.Soc.
  6. With H. Petyt and A. Zalloum: Appendix to "Constructing metric spaces from systems of walls". arXiv2404.12057.
  7. With H. Petyt and A. Zalloum: Hyperbolic models for CAT(0) spaces. arXiv2207.14127. Accepted in Advances in Mathematics
  8. With C. R. Abbott and T. Ng : Hierarchically hyperbolic groups and uniform exponential growth. arXiv1909.00439. Accepted in Mathematische Zeitschrift.
  9. 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.
  10. 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.
  11. With M. Cordes, J. Russell and A. Zalloum: Regularity of Morse geodesics and growth of stable subgroups. arXiv2008.06379. Accepted in Journal of Topology.
  12. With H. Petyt: Unbounded domains in hierarchically hyperbolic groups. arXiv2007.12535. Accepted in Groups, Geometry and Dynamics.
  13. With J. Russell and H. C. Tran: The local to global property for Morse quasi-geodesics. arXiv1908.11292. Accepted in Mathematische Zeitschrift.
  14. With J. Russell and H. C. Tran: Convexity in hierarchically hyperbolic spaces. arXiv:1809.09303. Accepted in Algebraic and Geometric Topology.
  15. Introduction to hyperbolic groups. Published version. Advances in Group Theory and Applications.
  16. With R. Kropholler: Closure Properties in the Class of Multiple Context Free Groups. arXiv1709.02478. Accepted in Groups Complexity Cryptology.
  17. With B. Robbio: Hierarchical hyperbolicity of hyperbolic-2-decomposable groups. arXiv2007.13383.
  18. Hyperbolic HHS II: Graphs of hierarchically hyperbolic groups. arXiv:1801.01850.
  19. Hyperbolic HHS I: Factor Systems and Quasi-convex subgroups. arXiv:1711.10931.

    20. 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?