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

Negative curvature in graphical small cancellation groups, joint with G. Arzhantseva, C. Cashen, and D. Hume, to appear in Groups Geom. Dyn. arXiv:1602.03767
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


Random triangular Burnside groups, joint with J. Mackay. arXiv:1810.01805
Divergence and quasi-isometry classes of random Gromov's monsters, joint with A. Sisto. arXiv:1805.04039
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

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 was a co-organizer of YGGT VII, which took place in Les Diablerets, Switzerland, in March 2018.


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