I am an Assistant Professor at ETH.
My main research area is geometric group theory, and
I'm especially interested in generalisations of hyperbolic groups.
Here is my CV (last update: October 2019).
You may wish to take a look at my blog.
E-mail: my-last-name (at) math.ethz.ch
Where to find me:
HG J 43
The Autumn 2019 Algebraic Topology I webpage is here: https://metaphor.ethz.ch/x/2019/fs/401-2554-00L/
I'm writing lecture notes on Geometric Group Theory. Please let me know if you have comments, corrections, complaints....
Last update: July 2014.
1) chapter on free subgroups of hyperbolic groups
(with Pierre Mathieu) Deviation inequalities and CLT for random walks on acylindrically hyperbolic groups
Accepted in Duke Mathematical Journal
(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.
Accepted in L'Enseignement Mathématique
(with Dominik Gruber and Romain Tessera) Gromov's random monsters do not act non-elementarily on hyperbolic spaces
Accepted in Proceedings of the AMS
(with John MacKay) Quasi-hyperbolic planes in relatively hyperbolic groups  [Blog post]
Accepted in Ann. Sci. Fenn.
(with Daniel Groves and Jason Manning) Boundaries of Dehn fillings
Accepted in Geometry & Topology
(with Jason Behrstock and Mark Hagen) Hierarchically hyperbolic spaces II: Combination theorems and the distance formula
Accepted in Pacific Journal of Mathematics
(with Tobias Hartnick) Bounded cohomology and virtually free hyperbolically embedded subgroups
Accepted in Groups, Geometry, and Dynamics
Many Haken Heegaard splittings
Accepted in Journal of Topology and Analysis
(with Federico Franceschini, Roberto Frigerio and Beatrice Pozzetti) The zero norm subspace of bounded cohomology of acylindrically hyperbolic groups
Accepted in Commentarii Mathematici Helvetici
(with Dominik Gruber) Infinitely presented graphical small cancellation groups are acylindrically hyperbolic
Accepted in Annales de L'Institut Fourier
(with Yago Antolin, Mahan Mj and Sam Taylor) Intersection properties of stable subgroups and bounded cohomology
Accteped in Indiana Univ. Math. J.
(with David Hume) Groups with no coarse embeddings into hyperbolic groups
NYJM 23 (2017), 1657-1670.
(with Joseph Maher) Random subgroups of acylindrically hyperbolic groups and hyperbolic embeddings
Accepted in IMRN
What is a hierarchically hyperbolic space?
[Blog post: Intro to HHSs][Talk: Intro to HHSs] [Talk: Intro to HHSs for cube complexes people]
Accepted in Proccedings of the "Beyond hyperbolicity" conference
(with Sam Taylor) Largest projections for random walks and shortest curves for random mapping tori
Accepted in Mathematical Research Letters
(with Matthew G. Durham and Mark Hagen) Boundaries and automorphisms of hierarchically hyperbolic spaces
Geometry & Topology 21 (2017), 3659-3758.
(with Jason Behrstock and Mark Hagen) Asymptotic dimension and small-cancellation for hierarchically hyperbolic spaces and groups
Proceedings of the LMS 114 (2017), 890-926.
(with Jason Behrstock and Mark Hagen) Hierarchically hyperbolic spaces I: curve complexes for cubical groups [Blog post: Intro to HHSs][Talk: Intro to HHSs] [Talk: Intro to HHSs for cube complexes people]
Geometry & Topology 21 (2017), 1731-1804.
(with Jason Behrstock, Mark Hagen and (appendix only) Pierre-Emmanuel Caprace) Thickness, relative hyperbolicity, and randomness in Coxeter groups
Here is the source code of the software associated with the paper. Please let us know if you have questions, comments, new data...
Algebraic & Geometric Topology 21 (2017), 1731-1804.
(with Yago Antolin and Ashot Minasyan) Commensurating endomorphisms of acylindrically hyperbolic groups and applications
Groups, Geometry, and Dynamics 10 (2016), 1149-1210.
(with Piotr Przytycki) A note on acylindrical hyperbolicity of Mapping Class Groups
Advanced Studies in Pure Mathematics, Hyperbolic Geometry and Geometric Group Theory conference proceedings, 255-264.
(with Roberto Frigerio and Beatrice Pozzetti) Extending higher dimensional quasi-cocycles
[Talk] [Talk: Overview of bounded cohomology of acylindrically hyperbolic groups]
Journal of Topology 8 (2015), 1123-1155.
Contracting elements and random walks  [Blog post]
Crelle's Journal 742 (2018), 79-114
(with Roberto Frigerio and Jean-François Lafont) Rigidity of high dimensional graph manifolds  [Blog post]
Asterisque 372 (2015), xxi+177 pp.
Tracking rates of random walks  [Blog post]
Israel Journal of Mathematics 220 (2017), 1-28.
Quasi-convexity of hyperbolically embedded subgroups
Mathematische Zeitschrift 283 (2016), 649-658.
(with Isaac Goldbring) The fundamental group of a locally finite graph with ends: a hyperfinite approach
Fundamenta Mathematicae 232 (2016), 21-39.
(with John MacKay) Embedding relatively hyperbolic groups in products of trees
Algebraic & Geometric Topology 13 (2013), 2261-2282.
(with Eduardo Martínez-Pedroza) Virtual amalgamation of relatively quasiconvex subgroups
Algebraic & Geometric Topology 12 (2012), 1993-2002.
Projections and relative hyperbolicity  [Blog post]
L'Enseignement Mathématique 59 (2013), 165-181.
(with David Hume) Embedding universal covers of graph manifolds in products of trees [Blog post]
Proceedings of the AMS 141 (2013), 3337-3340.
Tree-graded asymptotic cones
Groups, Geometry, and Dynamics 7 (2013), 697-735.
Separable and tree-like asymptotic cones of groups
Münster Journal of Mathematics 5 (2012), 233-248.
Exponential triples [or, my brush with ultrafilter combinatorics]
Electronic Journal of Combinatorics 18 (1) (2011).
(with Roberto Frigerio) Characterizing hyperbolic spaces and real trees
Geometriae Dedicata 142 (2009), 139-149.