On order units in the augmentation ideal [ arXiv ]
with Piotr Mizerka
Spectral gap for the cohomological Laplacian of SL_3(Z) [ arXiv ]
with Marek Kaluba and Piotr Mizerka
Higher Kazhdan projections, l_2-Betti numbers and Baum-Connes conjectures [ arXiv ]
with Sanaz Pooya and Kang Li
Expanders are counterexamples to the L_p-coarse Baum-Connes conjecture [ arXiv ]
with Yeong Chyuan Chung
To appear in the Journal of Noncommutative Geometry
On property (T) for Aut(F_n) and SL_n(Z)
with Marek Kaluba and Dawid Kielak
Annals of Mathematics, Vol. 193 (2021), Issue 2, p. 539--562 [ arXiv | journal ]
> Property (T) for Aut(F_n)
Extended abstract for Oberwolfach Reports [ pdf ]
Quasi-local algebras and asymptotic expanders
with Kang Li, Jan Špakula and Jiawen Zhang
Groups, Geometry and Dynamics, Volume 15, Issue 2, 2021, pp. 655–682 [ arXiv | journal ]
Group algebra criteria for vanishing of cohomology
with Uri Bader
Journal of Functional Analysis, Volume 279, Issue 11, 2020 [ arXiv | journal ]
Aut(F_5) has property (T)
with Marek Kaluba and Narutaka Ozawa
Mathematische Annalen, Volume 375 (2019), Issue 3--4, p 1169--1191 [ arXiv | journal ]
> Aut(F_5) has property (T)
Extended abstract in: Oberwolfach Reports Vol. 15, Issue 2, 2018, pp. 1117--1160 [ pdf | journal ]
Singular subgroups in A_2 groups and their von Neumann algebras [ arXiv | book chapter ]
with Yongle Jiang
In: Operator theory, operator algebras and their interactions with geometry and topology. Ronald G. Douglas memorial volume.
Operator Theory: Advances and Applications, 278. Birkhäuser/Springer 2020.
On complements of Kazhdan projections in semisimple groups
with Eric Reckwerdt
Studia Mathematica 246 (2019), p. 63--69 [ arXiv | journal ]
Certifying numerical estimates of spectral gaps
with Marek Kaluba
Groups Complexity Cryptology, Volume 10 (2018), Issue 1, p. 33--41 [ arXiv | journal ]
Kazhdan projections, random walks and ergodic theorems
with Cornelia Druţu
Journal für die reine und angewandte Mathematik (Crelle’s Journal), Volume 2019, Issue 754, Pages 49--86 [ arXiv | journal ]
> Kazhdan projections in Banach spaces
Extended abstract in: Oberwolfach Reports Vol. 12, Issue 1, (2015) 187--233 [ pdf | journal ]
Group 1-cohomology is complemented
Bulletin of the London Mathematical Society 49 (2017), no. 2, 216--219 [ arXiv | journal ]
Warped cones and spectral gaps
with Damian Sawicki
Proceedings of the American Mathematical Society 145 (2017), no. 2, 817--823 [ arXiv | journal ]
Eilenberg swindles and higher large scale homology of products of trees
with Francesca Diana
Groups, Geometry & Dynamics 11 (2017), no. 1, p. 371--392 [ arXiv | journal ]
Poincaré inequalities and rigidity for actions on Banach spaces
Journal of the European Mathematical Society (JEMS) 17 (2015), no. 3, 689--709 [ pdf | journal ]
Group Actions on Banach Spaces
In: Handbook of Group Actions, vol. II, 121--149. Edited by L. Ji, A. Papadopoulos, S.-T. Yau.
Advanced Lectures in Mathematics (ALM) 32, International Press, Somerville; Higher Education Press, Beijing, 2015 [ arXiv | publisher ]
Cohomology of deformations
with Uri Bader
Journal of Topology and Analysis 7 (2015), no. 1, 81--104 [ arXiv | journal ]
Aperiodic tilings of manifolds of intermediate growth
with Michał Marcinkowski
Groups, Geometry & Dynamics 8 (2014), no. 2, 479--483. [ arXiv | journal ]
Uniformly bounded representations and exact groups
with Kate Juschenko
Journal of Functional Analysis 266 (2014), no. 3, 1667--1673. [ arXiv | journal ]
Large Scale Geometry
Book written jointly with Guoliang Yu
EMS Textbooks in Mathematics, European Mathematical Society Publishing House, 2012.
Amenable actions, invariant means and bounded cohomology
with Jacek Brodzki, Graham A. Niblo and Nick Wright
Journal of Topology and Analysis 4 (2012), no. 3, 321--334. [ pdf | journal ]
A homological characterization of topological amenability
with Jacek Brodzki, Graham A. Niblo and Nick Wright
Algebraic & Geometric Topology 12 (2012), no. 3, 1767--1780. [ pdf | journal ]
Every finitely generated group is weakly exact
with Ronald G. Douglas
Journal of Functional Analysis 261 (2011), no. 12, 3723--3734. [ arXiv | journal ]
Diameters, distortion and eigenvalues
with Rostislav I. Grigorchuk
European Journal of Combinatorics 33 (2012), no. 7, 1574--1587. [ arXiv | journal ]
Residually finite actions and crossed products
with David Kerr
Ergodic Theory and Dynamical Systems, 32 (2012), no. 05, 1585-1614. [ arXiv | journal ]
Invariant expectations and vanishing of bounded cohomology for exact groups
with Ronald G. Douglas
Journal of Topology and Analysis 3 (2011), no. 1, 89--107. [ arXiv | journal ]
Hilbert C*-modules and amenable actions
with Ronald G. Douglas
Studia Mathematica 199 (2010), no. 2, 185--197. [ arXiv | journal ]
Controlled coarse homology and isoperimetric inequalities
with Ján Špakula
Journal of Topology 3 (2010), no. 2, 443--462. [ pdf | journal ]
Zero-in-the-spectrum conjecture on regular covers of compact manifolds
Commentarii Mathematici Helvetici 84 (2009), no. 1, 213--222. [ pdf | journal ]
Isoperimetry of group actions
Advances in Mathematics 219 (2008), no. 1, 1--26. [ pdf | journal ]
What is... Property A?
with Guoliang Yu
Notices of the American Mathematical Society 55 (2008), no. 4, 474--475. [ journal ]
Coarsely embeddable metric spaces without property A
Journal of Functional Analysis 252 (2007), no. 1, 126--136. [ pdf | journal ]
On exactness and isoperimetric profiles of discrete groups
Journal of Functional Analysis 243 (2007), no. 1, 323--344. [ pdf | journal ]
On coarse embeddability into l_p-spaces and a conjecture of Dranishnikov
Fundamenta Mathematicae 189 (2006), no. 2, 111--116. [ arXiv | journal ]
Group actions on Banach spaces and a geometric characterization of a-T-menability.
Topology and its Applications 153 (2006), no. 18, 3409--3412. [ arXiv | journal ]
Coarse embeddings of metric spaces into Banach spaces
Proceedings of the American Mathematical Society 133 (2005), no. 9, 2589--2596. [ arXiv | journal ]

I am interested primarily in geometric and analytic group theory and their intersection with index theory, non-commutative geometry and topology of manifolds.
Publications and preprints