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

Coboundary expansion and Gromov hyperbolicity    [ arXiv ]     

with Dawid Kielak

On (bi)reversible automata generating lamplighter groups    [ arXiv ]

with Veronika Prokhorchuk and Andriy Oliynyk

On order units in the augmentation ideal    [ arXiv ]

with Piotr Mizerka

To appear in the Proceedings of the American Mathematical Society

Spectral gap for the cohomological Laplacian of SL_3(Z)  [ arXiv ]

with Marek Kaluba and Piotr Mizerka

To appear in Experimental Mathematics

Higher Kazhdan projections, l_2-Betti numbers and Baum-Connes conjectures  

with Sanaz Pooya and Kang Li

Journal of Noncommutative Geometry 18 (2024), no. 1, pp. 313--336  [ arXiv | journal ]

Expanders are counterexamples to the L_p-coarse Baum-Connes conjecture

with Yeong Chyuan Chung

Journal of Noncommutative Geometry 17 (2023), no. 1, pp. 305–331  [ arXiv | journal ]

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 | journal ]


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   

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  [ arXiv | book chapter  ]

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.

[ First edition: 2012 ]   [ Second edition: 2023 ]

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 ]