Alessandro Sisto

Alessandro Sisto

I am an Assistant Professor at Heriot-Watt University.

My main research area is geometric group theory, and
I'm especially interested in generalisations of hyperbolic groups.
Here is some version of my CV (updated: August 2020).

I currently have three Phd students, Antoine Goldsborough, Giorgio Mangioni, and Stefanie Zbinden.

You may wish to take a look at my blog. If you're here because of HHSs, you may wish to have a look at the resources collected here.

E-mail: a.sisto at hw.ac.uk

Here are some incomplete lecture notes on Geometric Group Theory. Please let me know if you have comments, corrections, complaints....
Still missing:
1) chapter on free subgroups of hyperbolic groups
2) references

You can find all my papers and prerints here.

Papers and prerints since 2017

(with Antoine Goldsborough, Mark Hagen, and Harry Petyt, with an appendix by Jacob Russell) Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity

(with Mark Hagen and Giorgio Mangioni) A combinatorial structure for many hierarchically hyperbolic spaces

(with Matt Cordes and Stefanie Zbinden) Corrigendum to "Morse Boundaries of Proper Geodesic Metric Spaces"
Accepted in Groups, Geometry, and Dynamics.

(with Peter Feller and Gabriele Viaggi) Hyperbolic Heegaard splittings and Dehn twists

(with Elia Fioravanti, Annette Karrer, and Stefanie Zbinden) On the Čech cohomology of Morse boundaries

(with Antoine Goldsborough) Random divergence of groups

Appendix to: Property (NL) for group actions on hyperbolic spaces, by Sahana Balasubramanya, Francesco Fournier-Facio, and Anthony Genevois
Accepted in Groups, Geometry, and Dynamics

(with Giorgio Mangioni) Rigidity of mapping class groups mod powers of twists

(with Abdul Zalloum) Morse subsets of injective spaces are strongly contracting
Accepted in Groups, Geometry, and Dynamics

(with Uri Bader) Characterising acylindrical hyperbolicity via permutation actions

(with Mark Hagen, Jacob Russell, and Davide Spriano) Equivariant hierarchically hyperbolic structures for 3-manifold groups via quasimorphisms
Accepted in Annales de l'insitut Fourier

(with Mark Hagen) Some examples of separable convex-cocompact subgroups
Accepted in Bulletin of the LMS

(with Uri Bader, Pierre-Emmanuel Caprace, and Alex Furman) Hyperbolic actions of higher-rank lattices come from rank-one factors

The word problem for free groups cannot be solved in linear time*

(with Antoine Goldsborough) Markov chains on hyperbolic-like groups and quasi-isometries
Accepted in Crelle

(with Spencer Dowdall, Chris Leininger, and Matt Durham ) Extensions of Veech groups II: Hierarchical hyperbolicity and quasi-isometric rigidity
Accepted in Commentarii Mathematici Helvetici

(with Mark Hagen and Alexandre Martin) Extra-large type Artin groups are hierarchically hyperbolic
Accepted in Math. Annalen

(with John MacKay) Maps between relatively hyperbolic spaces and between their boundaries
Accepted in Transactions of the AMS

(with Matt Durham and Yair Minsky) Stable cubulations, bicombings, and barycenters
Accepted in Geometry & Topology

(with Adrien Boulanger, Pierre Mathieu, and Cagri Sert) Large deviations for random walks on hyperbolic spaces
Accepted in Annales scientifiques de l'École normale supérieure

(with Spencer Dowdall, Chris Leininger, and Matt Durham ) Extensions of Veech groups I: A hyperbolic action
Accepted in Journal of Topology

(with Peter Feller and Gabriele Viaggi) Uniform models and short curves for random 3-manifolds

(with Jason Behrstock, Mark Hagen, and Alexandre Martin) A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups

(with Roberto Frigerio) Central extensions and bounded cohomology
Accepted in Annales Henri Lebesgue

(with Ruth Charney and Matt Cordes) Complete topological descriptions of certain Morse boundaries
Groups, Geometry, and Dynamics 17, no. 1, 157-184.

(with François Dahmani and Mark Hagen) Dehn filling Dehn twists
Proc. Roy. Soc. Edinburgh Sect. A 151 (2021), no. 1, 28–51.

(with Dominik Gruber) Divergence and quasi-isometry classes of random Gromov's monsters
Math. Proc. Cambridge Philos. Soc. 171 (2021), no. 2, 249–264

(with Mladen Bestvina, Ken Bromberg and Koji Fujiwara) Acylindrical actions on projection complexes
Here is a shortened version of the paper still containing the main techniques and ideas.
Enseign. Math. 65 (2019), no. 1-2, 1–32.

What is a hierarchically hyperbolic space? [Blog post: Intro to HHSs][Talk: Intro to HHSs] [Talk: Intro to HHSs for cube complexes people]
London Math. Soc. Lecture Note Ser., 454, Cambridge Univ. Press, Cambridge, 2019.

(with Dominik Gruber and Romain Tessera) Gromov's random monsters do not act non-elementarily on hyperbolic spaces
Proc. Amer. Math. Soc. 148 (2020), no. 7, 2773–2782.

(with Jason Behrstock and Mark Hagen) Quasiflats in hierarchically hyperbolic spaces [Talk]
Duke Math. J. 170 (2021), no. 5, 909–996.

(with Federico Franceschini, Roberto Frigerio and Beatrice Pozzetti) The zero norm subspace of bounded cohomology of acylindrically hyperbolic groups
Comment. Math. Helv. 94 (2019), no. 1, 89–139.

(with David Hume) Groups with no coarse embeddings into hyperbolic groups
NYJM 23 (2017), 1657-1670.

(with Tobias Hartnick) Bounded cohomology and virtually free hyperbolically embedded subgroups
Groups Geom. Dyn. 13 (2019), no. 2, 677–694.

(with Joseph Maher) Random subgroups of acylindrically hyperbolic groups and hyperbolic embeddings
Int. Math. Res. Not. IMRN 2019, no. 13, 3941–3980.