Dominik Gruber


About me

I am an ETH Postdoctoral Fellow at the D-MATH at ETH Zürich. Before coming to Zürich, I did a one-year postdoc at Université de Neuchâtel. I finished my PhD at University of Vienna in 2015 under the supervision of Goulnara Arzhantseva.

Research interests

Geometric and analytic properties of groups
Gromov hyperbolic groups and generalizations
Small cancellation theory
Low-dimensional topology and CAT(0) geometry
Geometric and arithmetic constructions of expander graphs

Published or accepted papers

Infinitely presented graphical small cancellation groups are acylindrically hyperbolic, joint with A. Sisto, to appear in Ann. Inst. Fourier. arXiv:1408.4488
Characterizations of Morse quasi-geodesics via superlinear divergence and sublinear contraction, joint with G. Arzhantseva, C. Cashen, and D. Hume. Doc. Math. 22 (2017), 1193-1224.
Infinitely presented C(6)-groups are SQ-universal, J. London Math. Soc. 92 (2015), no. 1, 178-201. DOI
Finite index subgroups without unique product in graphical small cancellation groups, joint with A. Martin and M. Steenbock, Bull. London Math. Soc. 47 (2015), no. 4, 631-638. DOI
Groups with graphical C(6) and C(7) small cancellation presentations, Trans. Amer. Math. Soc. 367 (2015), no. 3, 2051-2078. DOI


Asymptotics of Cheeger constants and unitarisability of groups, joint with M. Gerasimova, N. Monod, and A. Thom. arXiv:1801.09600
Gromov's random monsters do not act non-elementarily on hyperbolic spaces, joint with A. Sisto and R. Tessera. arXiv:1705.10258
Small cancellation theory over Burnside groups, joint with R. Coulon. arXiv:1705.09651
Negative curvature in graphical small cancellation groups, joint with G. Arzhantseva, C. Cashen, and D. Hume. arXiv:1602.03767

My thesis

Infinitely presented graphical small cancellation groups: Coarse embeddings, acylindrical hyperbolicity, and subgroup constructions, PhD thesis, University of Vienna, 2015, 133 pages, permalink:


I am currently teaching a course 'Small cancellation theory' at ETH.


I am a co-organizer of YGGT VII, which will take place in Les Diablerets, Switzerland, in March 2018.

I gave talks at the following conferences:

Groups and geometry in the Southeast, London (UK), 2017, invited talk
Groups and computation, Hoboken (USA), 2017, invited talk
Groups of intermediate growth, amenability and related topics, Les Diablerets (Switzerland), 2017, invited talk
Non-positive curvature in action, Cambridge (UK), 2017, invited talk
Topological and homological methods in group theory, Bielefeld (Germany), 2016
Statistical physics on transitive graphs, Lausanne (Switzerland), 2015
Group theory and operator algebra, Bucharest (Romania), 2015, invited talk
Topics in geometric group theory, Bucharest (Romania), 2014, invited talk
Geometric, dynamical and combinatorial aspects of infinite groups, Rennes (France), 2014, invited talk
Young geometric group theory 3, Marseille (France), 2014
Geometric and analytic group theory, Ventotene (Italy), 2013
Geometric and asymptotic group theory with applications (GAGTA), New York (USA), 2013
Young geometric group theory 2, Haifa (Israel), 2013


My poster about graphical C(6) and C(7) small cancellation groups

Contact information

E-mail: dominik [dot] gruber [at] math [dot] ethz [dot] ch

Departement Mathematik
ETH Zürich
Rämistrasse 101
8092 Zürich, Switzerland