# 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
## Preprints

*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: http://ubdata.univie.ac.at/AC12717025
## Teaching

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

## Conferences

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

## Posters

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