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