Edit Profile (opens in new tab) Lubotzky, Alexander Co-Author Distance Author ID: lubotzky.alexander Published as: Lubotzky, Alexander; Lubotzky, A.; Lubotzky, Alex more...less External Links: MGP · Wikidata · GND · IdRef Videos: carmin.tv Documents Indexed: 182 Publications since 1979, including 5 Books and 16 Additional arXiv Preprints 4 Contributions as Editor Co-Authors: 115 Co-Authors with 143 Joint Publications 3,176 Co-Co-Authors all top 5 Co-Authors 40 single-authored 8 Kantor, William M. 8 Larsen, Michael Jeffrey 8 Mozes, Shahar 7 Magid, Andy Roy 7 Shalev, Aner 6 Bass, Hyman 5 Kassabov, Martin D. 5 Mann, Avinoam 5 Meiri, Chen 5 Samuels, Beth 5 Vishne, Uzi 5 Zimmer, Robert J. 4 Becker, Oren 4 Belolipetsky, Mikhail V. 4 Dinur, Irit 4 Evra, Shai 4 Guralnick, Robert Michael 4 Jarden, Moshe 4 Kaufman, Tali 4 Pyber, László 4 Reid, Alan W. 3 Meshulam, Roy 3 Nikolov, Nikolay Valeriev 3 Phillips, Ralph Saul 3 Sarnak, Peter Clive 2 Ben-Ezra, David El-Chai 2 Breuillard, Emmanuel 2 Capdeboscq, Inna 2 Dikstein, Yotam 2 Gelander, Tsachik 2 Glebsky, Lev Yu. 2 Goldfeld, Dorian Morris 2 Grunewald, Fritz J. 2 Haran, Dan 2 Kazhdan, David 2 Kontorovich, Alex V. 2 Levit, Arie 2 Livné, Ron A. 2 Long, D. Darren 2 Luria, Zur 2 Marion, Claude 2 Mosheiff, Jonathan 2 Parzanchevski, Ori 2 Raghunathan, Madabusi Santanam 2 Rogawski, Jonathan D. 2 Rosenthal, Ron 2 Segal, Daniel 2 Thom, Andreas Berthold 2 Tiep Pham Huu 2 Venkataramana, Tyakal Nanjundiah 2 Weinberger, Shmuel 1 Abért, Miklós 1 Aravinda, C. S. 1 Avni, Nir 1 Babai, László 1 Bader, Uri 1 Bekka, Mohammed el Bachir 1 Birman, Joan S. 1 Bleher, Frauke M. 1 Böge, Sigrid 1 Borovik, Alexandre V. 1 Bowen, Lewis Phylip 1 Burger, Marc 1 Cappell, Sylvain E. 1 Cheetham-West, Tamunonye 1 Chinburg, Ted 1 Conder, Marston Donald Edward 1 De Chiffre, Marcus 1 de Cornulier, Yves 1 du Sautoy, Marcus 1 Farb, Benson 1 Fisher, David Michael 1 Garion, Shelly 1 Goldman, William M. 1 Golubev, Konstantin 1 Gongopadhyay, Krishnendu 1 Grigorchuk, Rostislav Ivanovich 1 Guth, Lawrence David 1 Hrushovski, Ehud 1 Jaikin-Zapirain, Andrei 1 Kowalski, Emmanuel 1 Kozma, Gady 1 Kropholler, Peter H. 1 Long, Darren D. 1 Lubetzky, Eyal 1 Maher, Joseph 1 Malestein, Justin 1 Manning, Jason Fox 1 Margulis, Grigoriĭ Aleksandrovich 1 Martin, Benjamin M. S. 1 McCarthy, John D. 1 Minsky, Yair N. 1 Mj, Mahan 1 Monod, Nicolas 1 Myasnikov, Alexei G. 1 Neftin, Danny 1 Oppenheim, Izhar 1 Pak, Igor 1 Rangarajan, Bharatram 1 Rémy, Bertrand ...and 16 more Co-Authors all top 5 Serials 16 Journal of Algebra 13 Israel Journal of Mathematics 5 Duke Mathematical Journal 5 Geometric and Functional Analysis. GAFA 5 Journal of the European Mathematical Society (JEMS) 5 Groups, Geometry, and Dynamics 4 American Journal of Mathematics 4 Bulletin of the London Mathematical Society 4 Geometriae Dedicata 4 Inventiones Mathematicae 4 Journal of the American Mathematical Society 4 Bulletin of the American Mathematical Society. New Series 4 Annals of Mathematics. Second Series 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Advances in Mathematics 3 European Journal of Combinatorics 3 Notices of the American Mathematical Society 3 Journal of Group Theory 3 Progress in Mathematics 2 Communications on Pure and Applied Mathematics 2 Journal d’Analyse Mathématique 2 Acta Mathematica 2 Commentarii Mathematici Helvetici 2 Proceedings of the American Mathematical Society 2 Proceedings of the London Mathematical Society. Third Series 2 Transactions of the American Mathematical Society 2 International Journal of Algebra and Computation 2 Proceedings of the National Academy of Sciences of the United States of America 2 Transformation Groups 1 Journal of Mathematical Physics 1 Archiv der Mathematik 1 Glasgow Mathematical Journal 1 Illinois Journal of Mathematics 1 Publications Mathématiques 1 Journal of Combinatorial Theory. Series B 1 Journal of Functional Analysis 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Publicationes Mathematicae Debrecen 1 The Quarterly Journal of Mathematics. Oxford Second Series 1 Topology 1 Ergodic Theory and Dynamical Systems 1 Combinatorica 1 Discrete & Computational Geometry 1 SIAM Journal on Discrete Mathematics 1 IMRN. International Mathematics Research Notices 1 L’Enseignement Mathématique. 2e Série 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Pure and Applied Mathematics Quarterly 1 Contemporary Mathematics 1 Proceedings of the Steklov Institute of Mathematics 1 Algebra & Number Theory 1 Journal of Topology 1 Japanese Journal of Mathematics. 3rd Series 1 Bulletin of Mathematical Sciences 1 Forum of Mathematics, Sigma 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Modern Birkhäuser Classics all top 5 Fields 126 Group theory and generalizations (20-XX) 53 Topological groups, Lie groups (22-XX) 36 Combinatorics (05-XX) 32 Number theory (11-XX) 14 Manifolds and cell complexes (57-XX) 8 Algebraic geometry (14-XX) 8 Abstract harmonic analysis (43-XX) 6 Computer science (68-XX) 5 Field theory and polynomials (12-XX) 5 Functions of a complex variable (30-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Probability theory and stochastic processes (60-XX) 4 General and overarching topics; collections (00-XX) 4 Geometry (51-XX) 3 Algebraic topology (55-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Information and communication theory, circuits (94-XX) 2 History and biography (01-XX) 2 Mathematical logic and foundations (03-XX) 2 Commutative algebra (13-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 \(K\)-theory (19-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Functional analysis (46-XX) 2 Quantum theory (81-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Nonassociative rings and algebras (17-XX) 1 Measure and integration (28-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 162 Publications have been cited 4,054 times in 2,700 Documents Cited by ▼ Year ▼ Ramanujan graphs. Zbl 0661.05035 Lubotzky, A.; Phillips, R.; Sarnak, P. 533 1988 Discrete groups, expanding graphs and invariant measures. Appendix by Jonathan D. Rogawski. Zbl 0826.22012 Lubotzky, Alexander 223 1994 Subgroup growth. Zbl 1071.20033 Lubotzky, Alexander; Segal, Dan 173 2003 Varieties of representations of finitely generated groups. Zbl 0598.14042 Lubotzky, Alexander; Magid, Andy R. 164 1985 Powerful \(p\)-groups. I: Finite groups. Zbl 0626.20010 Lubotzky, Alexander; Mann, Avinoam 137 1987 Abelian and solvable subgroups of the mapping class group. Zbl 0551.57004 Birman, Joan S.; Lubotzky, Alex; McCarthy, John 106 1983 The probability of generating a finite classical group. Zbl 0718.20011 Kantor, William M.; Lubotzky, Alexander 98 1990 Expander graphs in pure and applied mathematics. Zbl 1232.05194 Lubotzky, Alexander 89 2012 Discrete groups, expanding graphs and invariant measures. With an appendix by Jonathan D. Rogawski. Reprint of the 1994 original. Zbl 1183.22001 Lubotzky, Alexander 77 2010 Hecke operators and distributing points on the sphere. I. Zbl 0619.10052 Lubotzky, A.; Phillips, R.; Sarnak, P. 63 1986 The word and Riemannian metrics on lattices of semisimple groups. Zbl 0988.22007 Lubotzky, Alexander; Mozes, Shahar; Raghunathan, M. S. 62 2000 Ramanujan complexes of type \(\widetilde A_d\). Zbl 1087.05036 Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi 59 2005 Tree lattices. With appendices by H. Bass, L. Carbone, A. Lubotzky, G. Rosenberg, and J. Tits. Zbl 1053.20026 Bass, Hyman; Lubotzky, Alexander 54 2001 Groups and expanders. Zbl 0787.05049 Lubotzky, A.; Weiss, B. 52 1993 Cayley graphs: Eigenvalues, expanders and random walks. Zbl 0835.05033 Lubotzky, Alexander 51 1995 Subgroup growth and congruence subgroups. Zbl 0848.20036 Lubotzky, Alexander 50 1995 Hecke operators and distributing points on \(S^2\). II. Zbl 0648.10034 Lubotzky, A.; Phillips, R.; Sarnak, P. 50 1987 Explicit constructions of Ramanujan complexes of type \(\widetilde A_d\). Zbl 1135.05038 Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi 49 2005 Lattices in rank one Lie groups over local fields. Zbl 0786.22017 Lubotzky, Alexander 43 1991 Powerful \(p\)-groups. II: \(p\)-adic analytic groups. Zbl 0626.20022 Lubotzky, Alexander; Mann, Avinoam 43 1987 Group presentation, p-adic analytic groups and lattices in \(SL_ 2({\mathbb{C}})\). Zbl 0541.20020 Lubotzky, Alexander 36 1983 Free quotients and the first Betti number of some hyperbolic manifolds. Zbl 0876.22015 Lubotzky, Alexander 35 1996 Rank-1 phenomena for mapping class groups. Zbl 1025.20023 Farb, Benson; Lubotzky, Alexander; Minsky, Yair 35 2001 Combinatorial group theory for pro-p groups. Zbl 0489.20024 Lubotzky, Alexander 35 1982 Small-diameter Cayley graphs for finite simple groups. Zbl 0702.05042 Babai, L.; Kantor, W. M.; Lubotzky, A. 34 1989 Finitely generated groups of polynomial subgroup growth. Zbl 0811.20027 Lubotzky, Alexander; Mann, Avinoam; Segal, Dan 33 1993 Representation growth of linear groups. Zbl 1142.22006 Larsen, Michael; Lubotzky, Alexander 33 2008 On some \(\Lambda\)-analytic pro-\(p\) groups. Zbl 0819.20030 Lubotzky, Alexander; Shalev, Aner 32 1994 Normal automorphisms of free groups. Zbl 0432.20025 Lubotzky, Alexander 32 1980 Linear representations of the automorphism group of a free group. Zbl 1175.20028 Grunewald, Fritz; Lubotzky, Alexander 32 2009 The product replacement algorithm and Kazhdan’s property (T). Zbl 0980.20078 Lubotzky, Alexander; Pak, Igor 32 2001 Invariable generation and the Chebotarev invariant of a finite group. Zbl 1248.20036 Kantor, W. M.; Lubotzky, A.; Shalev, A. 32 2011 High dimensional expanders. Zbl 1448.05125 Lubotzky, Alexander 31 2018 Subgroups of free profinite groups and large subfields of Q. Zbl 0485.20021 Lubotzky, Alexander; van den Dries, Lou 31 1981 Arithmetic quotients of the mapping class group. Zbl 1334.57017 Grunewald, Fritz; Larsen, Michael; Lubotzky, Alexander; Malestein, Justin 30 2015 Isoperimetric inequalities for Ramanujan complexes and topological expanders. Zbl 1339.05075 Kaufman, Tali; Kazhdan, David; Lubotzky, Alexander 30 2016 On groups of polynomial subgroup growth. Zbl 0743.20040 Lubotzky, Alexander; Mann, Avinoam 29 1991 Stability, cohomology vanishing, and nonapproximable groups. Zbl 1456.22002 De Chiffre, Marcus; Glebsky, Lev; Lubotzky, Alexander; Thom, Andreas 29 2020 Ramanujan complexes and high dimensional expanders. Zbl 1302.05095 Lubotzky, Alexander 28 2014 Counting hyperbolic manifolds. Zbl 1029.57021 Burger, M.; Gelander, T.; Lubotzky, A.; Mozes, S. 28 2002 Pro-finite presentations. Zbl 0985.20017 Lubotzky, Alexander 27 2001 Stability and invariant random subgroups. Zbl 1516.20007 Becker, Oren; Lubotzky, Alexander; Thom, Andreas 27 2019 Finite simple groups as expanders. Zbl 1161.20010 Kassabov, Martin; Lubotzky, Alexander; Nikolov, Nikolay 26 2006 Presentations of finite simple groups: profinite and cohomological approaches. Zbl 1135.20024 Guralnick, Robert; Kantor, William M.; Kassabov, Martin; Lubotzky, Alexander 25 2007 Polynomial representation growth and the congruence subgroup problem. Zbl 1134.20056 Lubotzky, Alexander; Martin, Benjamin 24 2004 A group theoretic characterization of linear groups. Zbl 0647.20045 Lubotzky, Alexander 24 1988 Automorphisms of groups and of schemes of finite type. Zbl 0517.14015 Bass, Hyman; Lubotzky, Alexander 24 1983 Residually finite groups of finite rank. Zbl 0696.20031 Lubotzky, Alexander; Mann, Avinoam 24 1989 Free quotients and the congruence kernel of \(SL_ 2\). Zbl 0495.20021 Lubotzky, Alexander 23 1982 Presentations of finite simple groups: a quantitative approach. Zbl 1223.20024 Guralnick, R. M.; Kantor, W. M.; Kassabov, M.; Lubotzky, A. 23 2008 Eigenvalues of the Laplacian, the first Betti number and the congruence subgroup problem. Zbl 0885.11037 Lubotzky, Alexander 22 1996 Counting arithmetic lattices and surfaces. Zbl 1214.22002 Belolipetsky, Mikhail; Gelander, Tsachik; Lubotzky, Alexander; Shalev, Aner 22 2010 Finite groups and hyperbolic manifolds. Zbl 1113.57007 Belolipetsky, Mikhail; Lubotzky, Alexander 22 2005 Variants of Kazhdan’s property for subgroups of semisimple groups. Zbl 0706.22010 Lubotzky, Alexander; Zimmer, Robert J. 21 1989 The proalgebraic completion of rigid groups. Zbl 1059.20036 Bass, Hyman; Lubotzky, Alexander; Magid, Andy R.; Mozes, Shahar 21 2002 The expected number of random elements to generate a finite group. Zbl 1042.20047 Lubotzky, Alexander 21 2002 Finite representations in the unitary dual and Ramanujan groups. Zbl 1080.22006 Lubotzky, Alexander; Shalom, Yehuda 20 2004 Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds. Zbl 1298.81052 Guth, Larry; Lubotzky, Alexander 19 2014 Cyclic subgroups of exponential growth and metrics on discrete groups. Zbl 0786.22016 Lubotzky, Alexander; Mozes, Shahar; Raghunathan, M. S. 18 1993 High dimensional expanders and property testing. Zbl 1365.68462 Kaufman, Tali; Lubotzky, Alexander 18 2014 Linear-central filtrations on groups. Zbl 0817.20038 Bass, Hyman; Lubotzky, Alexander 17 1994 Nonarithmetic superrigid groups: Counterexamples to Platonov’s conjecture. Zbl 0963.22005 Bass, Hyman; Lubotzky, Alexander 17 2000 Counting finite index subgroups. Zbl 0862.20020 Lubotzky, Alexander 16 1995 Images of word maps in finite simple groups. Zbl 1318.20014 Lubotzky, Alexander 16 2014 Invariable generation of infinite groups. Zbl 1318.20032 Kantor, William M.; Lubotzky, Alexander; Shalev, Aner 16 2015 Cohomology of unipotent and prounipotent groups. Zbl 0473.20031 Lubotzky, Alexander; Magid, Andy R. 16 1982 Mixing properties and the chromatic number of Ramanujan complexes. Zbl 1328.05208 Evra, Shai; Golubev, Konstantin; Lubotzky, Alexander 15 2015 Dynamics and \(\operatorname{Aut}(F_N)\) actions on group presentations and representations. Zbl 1266.20045 Lubotzky, Alexander 15 2011 Group stability and property (T). Zbl 1516.20100 Becker, Oren; Lubotzky, Alexander 15 2020 Functional equations and uniformity for local zeta functions of nilpotent groups. Zbl 0864.20020 Du Sautoy, Marcus P. F.; Lubotzky, Alexander 14 1996 Presentations of finite simple groups: a computational approach. Zbl 1256.20008 Guralnick, R. M.; Kantor, W. M.; Kassabov, M.; Lubotzky, A. 14 2011 Beauville surfaces and finite simple groups. Zbl 1255.20008 Garion, Shelly; Larsen, Michael; Lubotzky, Alexander 14 2012 Superrigidity for the commensurability group of tree lattices. Zbl 0839.22011 Lubotzky, A.; Mozes, S.; Zimmer, R. J. 13 1994 Expansion of building-like complexes. Zbl 1405.55019 Lubotzky, Alexander; Meshulam, Roy; Mozes, Shahar 13 2016 Random Latin squares and 2-dimensional expanders. Zbl 1306.05020 Lubotzky, Alexander; Meshulam, Roy 13 2015 Dimension expanders. Zbl 1154.15002 Lubotzky, Alexander; Zelmanov, Efim 13 2008 Subgroup growth of lattices in semisimple Lie groups. Zbl 1145.22004 Lubotzky, Alexander; Nikolov, Nikolay 12 2004 Lattices of minimal covolume in \(\mathrm{SL}_ 2\): a nonarchimedean analogue of Siegel’s theorem \(\mu\geq \pi /21\). Zbl 0731.22009 Lubotzky, Alexander 12 1990 Enumerating boundedly generated finite groups. Zbl 1052.20017 Lubotzky, Alexander 12 2001 On finite index subgroups of linear groups. Zbl 0597.20043 Lubotzky, Alexander 12 1987 Trees and discrete subgroups of Lie groups over local fields. Zbl 0676.22007 Lubotzky, Alexander 11 1989 Division algebras and noncommensurable isospectral manifolds. Zbl 1123.58020 Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi 11 2006 Deformation theory and finite simple quotients of triangle groups. I. Zbl 1312.20030 Larsen, Michael; Lubotzky, Alexander; Marion, Claude 11 2014 Sieve methods in group theory. I: Powers in linear groups. Zbl 1283.20075 Lubotzky, Alexander; Meiri, Chen 11 2012 Embedding covers and the theory of Frobenius fields. Zbl 0502.20013 Haran, Dan; Lubotzky, Alexander 11 1982 Discrete groups of slow subgroup growth. Zbl 0877.20019 Lubotzky, Alexander; Pyber, László; Shalev, Aner 10 1996 Counting congruence subgroups. Zbl 1159.20329 Goldfeld, Dorian; Lubotzky, Alexander; Pyber, László 10 2004 Random methods in 3-manifold theory. Zbl 1354.57026 Lubotzky, Alexander; Maher, Joseph; Wu, Conan 10 2016 Not every uniform tree covers Ramanujan graphs. Zbl 1024.05021 Lubotzky, Alexander; Nagnibeda, Tatiana 10 1998 First order rigidity of non-uniform higher rank arithmetic groups. Zbl 1454.20001 Avni, Nir; Lubotzky, Alexander; Meiri, Chen 10 2019 A Moore bound for simplicial complexes. Zbl 1180.13028 Lubotzky, Alexander; Meshulam, Roy 10 2007 Heegaard genus and property \({\tau}\) for hyperbolic 3-manifolds. Zbl 1158.57018 Long, D. D.; Lubotzky, A.; Reid, A. W. 10 2008 Powers in finitely generated groups. Zbl 0871.20038 Hrushovski, E.; Kropholler, P. H.; Lubotzky, A.; Shalev, A. 9 1996 Edge transitive Ramanujan graphs and symmetric LDPC good codes. Zbl 1286.94102 Kaufman, Tali; Lubotzky, Alexander 9 2012 Free prounipotent groups. Zbl 0503.20008 Lubotzky, Alexander; Magid, Andy R. 9 1983 Finite simple groups of Lie type as expanders. Zbl 1257.20016 Lubotzky, Alexander 9 2011 Bounded generation and linear groups. Zbl 1059.20048 Abért, Miklós; Lubotzky, Alexander; Pyber, László 9 2003 Dimension function for discrete groups. Zbl 0605.20029 Lubotzky, Alexander 9 1986 Lattices of minimal covolume in \(\text{SL}_2\) over local fields. Zbl 1026.22013 Lubotzky, A.; Weigel, Th. 9 1999 What is \(\dots\) a thin group? Zbl 1423.20060 Kontorovich, Alex; Long, D. Darren; Lubotzky, Alexander; Reid, Alan W. 9 2019 Sylow-conjugate number fields. Zbl 1546.11167 Lubotzky, Alexander; Neftin, Danny 1 2023 Locally testable codes with constant rate, distance, and locality. Zbl 07774345 Dinur, Irit; Evra, Shai; Livne, Ron; Lubotzky, Alexander; Mozes, Shahar 7 2022 Uncountably many permutation stable groups. Zbl 1512.20102 Levit, Arie; Lubotzky, Alexander 5 2022 Infinitely presented permutation stable groups and invariant random subgroups of metabelian groups. Zbl 07543353 Levit, Arie; Lubotzky, Alexander 4 2022 Expansion in simple groups. Zbl 1516.22006 Breuillard, Emmanuel; Lubotzky, Alexander 2 2022 Constructing highly regular expanders from hyperbolic Coxeter groups. Zbl 1514.20138 Conder, Marston; Lubotzky, Alexander; Schillewaert, Jeroen; Thilmany, François 1 2022 On the asymptotic number of generators of high rank arithmetic lattices. Zbl 1521.22008 Lubotzky, Alexander; Slutsky, Raz 1 2022 Stability, cohomology vanishing, and nonapproximable groups. Zbl 1456.22002 De Chiffre, Marcus; Glebsky, Lev; Lubotzky, Alexander; Thom, Andreas 29 2020 Group stability and property (T). Zbl 1516.20100 Becker, Oren; Lubotzky, Alexander 15 2020 Non \(p\)-norm approximated groups. Zbl 1500.22008 Lubotzky, Alexander; Oppenheim, Izhar 9 2020 Random walks on Ramanujan complexes and digraphs. Zbl 1454.05114 Lubetzky, E.; Lubotzky, A.; Parzanchevski, O. 9 2020 From Ramanujan graphs to Ramanujan complexes. Zbl 1462.05235 Lubotzky, Alexander; Parzanchevski, Ori 3 2020 Group actions in ergodic theory, geometry, and topology. Selected papers. Edited by David Fisher. With a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis. Zbl 1435.22001 Zimmer, Robert J. 1 2020 Stability and invariant random subgroups. Zbl 1516.20007 Becker, Oren; Lubotzky, Alexander; Thom, Andreas 27 2019 First order rigidity of non-uniform higher rank arithmetic groups. Zbl 1454.20001 Avni, Nir; Lubotzky, Alexander; Meiri, Chen 10 2019 What is \(\dots\) a thin group? Zbl 1423.20060 Kontorovich, Alex; Long, D. Darren; Lubotzky, Alexander; Reid, Alan W. 9 2019 Random Steiner systems and bounded degree coboundary expanders of every dimension. Zbl 1426.05183 Lubotzky, Alexander; Luria, Zur; Rosenthal, Ron 8 2019 Generalized triangle groups, expanders, and a problem of Agol and Wise. Zbl 1468.20083 Lubotzky, Alexander; Manning, Jason Fox; Wilton, Henry 4 2019 Counting non-uniform lattices. Zbl 1425.22009 Belolipetsky, Mikhail; Lubotzky, Alexander 2 2019 The congruence topology, Grothendieck duality and thin groups. Zbl 1448.11080 Lubotzky, Alexander; Venkataramana, Tyakal Nanjundiah 2 2019 Linear representations of random groups. Zbl 1469.20014 Kozma, Gady; Lubotzky, Alexander 2 2019 High dimensional expanders. Zbl 1448.05125 Lubotzky, Alexander 31 2018 The congruence subgroup problem for low rank free and free metabelian groups. Zbl 1386.20027 Ben-Ezra, David El-Chai; Lubotzky, Alexander 4 2018 A trichotomy theorem for transformation groups of locally symmetric manifolds and topological rigidity. Zbl 1403.22012 Cappell, Sylvain; Lubotzky, Alexander; Weinberger, Shmuel 1 2018 On groups and simplicial complexes. Zbl 1384.05187 Lubotzky, Alexander; Luria, Zur; Rosenthal, Ron 1 2018 Good cyclic codes and the uncertainty principle. Zbl 1436.94116 Evra, Shai; Kowalski, Emmanuel; Lubotzky, Alexander 4 2017 Isoperimetric inequalities for Ramanujan complexes and topological expanders. Zbl 1339.05075 Kaufman, Tali; Kazhdan, David; Lubotzky, Alexander 30 2016 Expansion of building-like complexes. Zbl 1405.55019 Lubotzky, Alexander; Meshulam, Roy; Mozes, Shahar 13 2016 Random methods in 3-manifold theory. Zbl 1354.57026 Lubotzky, Alexander; Maher, Joseph; Wu, Conan 10 2016 Presentations: from Kac-Moody groups to profinite and back. Zbl 1472.20117 Capdeboscq, I.; Lubotzky, A.; Rémy, B. 2 2016 Sliceable groups and towers of fields. Zbl 1368.20023 Böge, Sigrid; Jarden, Moshe; Lubotzky, Alexander 1 2016 Arithmetic quotients of the mapping class group. Zbl 1334.57017 Grunewald, Fritz; Larsen, Michael; Lubotzky, Alexander; Malestein, Justin 30 2015 Invariable generation of infinite groups. Zbl 1318.20032 Kantor, William M.; Lubotzky, Alexander; Shalev, Aner 16 2015 Mixing properties and the chromatic number of Ramanujan complexes. Zbl 1328.05208 Evra, Shai; Golubev, Konstantin; Lubotzky, Alexander 15 2015 Random Latin squares and 2-dimensional expanders. Zbl 1306.05020 Lubotzky, Alexander; Meshulam, Roy 13 2015 Geometry, groups and dynamics. ICTS program: groups, geometry and dynamics, Almora, India, December 3–16, 2012. Zbl 1318.30003 2 2015 Ramanujan complexes and high dimensional expanders. Zbl 1302.05095 Lubotzky, Alexander 28 2014 Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds. Zbl 1298.81052 Guth, Larry; Lubotzky, Alexander 19 2014 High dimensional expanders and property testing. Zbl 1365.68462 Kaufman, Tali; Lubotzky, Alexander 18 2014 Images of word maps in finite simple groups. Zbl 1318.20014 Lubotzky, Alexander 16 2014 Deformation theory and finite simple quotients of triangle groups. I. Zbl 1312.20030 Larsen, Michael; Lubotzky, Alexander; Marion, Claude 11 2014 Deformation theory and finite simple quotients of triangle groups. II. Zbl 1312.20031 Larsen, Michael; Lubotzky, Alexander; Marion, Claude 7 2014 Finiteness properties and profinite completions. Zbl 1295.20029 Lubotzky, Alexander 5 2014 The Galois group of random elements of linear groups. Zbl 1304.11125 Lubotzky, Alexander; Rosenzweig, Lior 4 2014 On conjugacy growth of linear groups. Zbl 1278.20064 Breuillard, Emmanuel; Cornulier, Yves; Lubotzky, Alexander; Meiri, Chen 8 2013 Representation varieties of Fuchsian groups. Zbl 1272.20054 Larsen, Michael; Lubotzky, Alexander 7 2013 Expander graphs in pure and applied mathematics. Zbl 1232.05194 Lubotzky, Alexander 89 2012 Beauville surfaces and finite simple groups. Zbl 1255.20008 Garion, Shelly; Larsen, Michael; Lubotzky, Alexander 14 2012 Sieve methods in group theory. I: Powers in linear groups. Zbl 1283.20075 Lubotzky, Alexander; Meiri, Chen 11 2012 Edge transitive Ramanujan graphs and symmetric LDPC good codes. Zbl 1286.94102 Kaufman, Tali; Lubotzky, Alexander 9 2012 Manifolds counting and class field towers. Zbl 1241.22014 Belolipetsky, Mikhail; Lubotzky, Alexander 8 2012 Sieve methods in group theory. II: The mapping class group. Zbl 1284.57017 Lubotzky, Alexander; Meiri, Chen 7 2012 Sieve methods in group theory. III: \(\operatorname{Aut}(F_n)\). Zbl 1284.20035 Lubotzky, Alexander; Meiri, Chen 3 2012 Invariable generation and the Chebotarev invariant of a finite group. Zbl 1248.20036 Kantor, W. M.; Lubotzky, A.; Shalev, A. 32 2011 Dynamics and \(\operatorname{Aut}(F_N)\) actions on group presentations and representations. Zbl 1266.20045 Lubotzky, Alexander 15 2011 Presentations of finite simple groups: a computational approach. Zbl 1256.20008 Guralnick, R. M.; Kantor, W. M.; Kassabov, M.; Lubotzky, A. 14 2011 Finite simple groups of Lie type as expanders. Zbl 1257.20016 Lubotzky, Alexander 9 2011 Lattices with and lattices without spectral gap. Zbl 1239.22003 Bekka, Bachir; Lubotzky, Alexander 5 2011 Remarks on proficient groups. Zbl 1239.20037 Guralnick, R. M.; Kantor, W. M.; Kassabov, M.; Lubotzky, A. 1 2011 Discrete groups, expanding graphs and invariant measures. With an appendix by Jonathan D. Rogawski. Reprint of the 1994 original. Zbl 1183.22001 Lubotzky, Alexander 77 2010 Counting arithmetic lattices and surfaces. Zbl 1214.22002 Belolipetsky, Mikhail; Gelander, Tsachik; Lubotzky, Alexander; Shalev, Aner 22 2010 Linear representations of the automorphism group of a free group. Zbl 1175.20028 Grunewald, Fritz; Lubotzky, Alexander 32 2009 On non-uniform Ramanujan complexes. Zbl 1279.11053 Samuels, Beth 3 2009 Representation growth of linear groups. Zbl 1142.22006 Larsen, Michael; Lubotzky, Alexander 33 2008 Presentations of finite simple groups: a quantitative approach. Zbl 1223.20024 Guralnick, R. M.; Kantor, W. M.; Kassabov, M.; Lubotzky, A. 23 2008 Dimension expanders. Zbl 1154.15002 Lubotzky, Alexander; Zelmanov, Efim 13 2008 Heegaard genus and property \({\tau}\) for hyperbolic 3-manifolds. Zbl 1158.57018 Long, D. D.; Lubotzky, A.; Reid, A. W. 10 2008 Elementary equivalence of profinite groups. Zbl 1200.20023 Jarden, Moshe; Lubotzky, Alexander 9 2008 Presentations of finite simple groups: profinite and cohomological approaches. Zbl 1135.20024 Guralnick, Robert; Kantor, William M.; Kassabov, Martin; Lubotzky, Alexander 25 2007 A Moore bound for simplicial complexes. Zbl 1180.13028 Lubotzky, Alexander; Meshulam, Roy 10 2007 Finite simple groups as expanders. Zbl 1161.20010 Kassabov, Martin; Lubotzky, Alexander; Nikolov, Nikolay 26 2006 Division algebras and noncommensurable isospectral manifolds. Zbl 1123.58020 Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi 11 2006 Isospectral Cayley graphs of some finite simple groups. Zbl 1110.05044 Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi 8 2006 On presentations and second cohomology of some finite simple groups. Zbl 1123.20030 Korchagina, Inna; Lubotzky, Alexander 3 2006 Ramanujan complexes of type \(\widetilde A_d\). Zbl 1087.05036 Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi 59 2005 Explicit constructions of Ramanujan complexes of type \(\widetilde A_d\). Zbl 1135.05038 Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi 49 2005 Finite groups and hyperbolic manifolds. Zbl 1113.57007 Belolipetsky, Mikhail; Lubotzky, Alexander 22 2005 Finite representations of adelic groups, the congruence kernel and cohomology of finite simple groups. Zbl 1188.20046 Lubotzky, Alexander 7 2005 What is …property \((\tau)\)? Zbl 1101.22300 Lubotzky, Alex 5 2005 Some more non-arithmetic rigid groups. Zbl 1084.22007 Lubotzky, Alexander 5 2005 The finitary Andrews-Curtis conjecture. Zbl 1114.20011 Borovik, Alexandre V.; Lubotzky, Alexander; Myasnikov, Alexei G. 3 2005 Polynomial representation growth and the congruence subgroup problem. Zbl 1134.20056 Lubotzky, Alexander; Martin, Benjamin 24 2004 Finite representations in the unitary dual and Ramanujan groups. Zbl 1080.22006 Lubotzky, Alexander; Shalom, Yehuda 20 2004 Subgroup growth of lattices in semisimple Lie groups. Zbl 1145.22004 Lubotzky, Alexander; Nikolov, Nikolay 12 2004 Counting congruence subgroups. Zbl 1159.20329 Goldfeld, Dorian; Lubotzky, Alexander; Pyber, László 10 2004 Normal subgroup growth of linear groups: the \((G_2,F_4,E_8)\)-theorem. Zbl 1161.20305 Larsen, Michael; Lubotzky, Alexander 8 2004 Counting primes, groups, and manifolds. Zbl 1139.11324 Goldfeld, Dorian; Lubotzky, Alexander; Nikolov, Nikolay; Pyber, László 7 2004 The mathematics of Boris Weisfeiler. Zbl 1159.01340 Lubotzky, Alexander 1 2004 Subgroup growth. Zbl 1071.20033 Lubotzky, Alexander; Segal, Dan 173 2003 Bounded generation and linear groups. Zbl 1059.20048 Abért, Miklós; Lubotzky, Alexander; Pyber, László 9 2003 Counting hyperbolic manifolds. Zbl 1029.57021 Burger, M.; Gelander, T.; Lubotzky, A.; Mozes, S. 28 2002 The proalgebraic completion of rigid groups. Zbl 1059.20036 Bass, Hyman; Lubotzky, Alexander; Magid, Andy R.; Mozes, Shahar 21 2002 The expected number of random elements to generate a finite group. Zbl 1042.20047 Lubotzky, Alexander 21 2002 A group theoretical characterisation of S-arithmetic groups in higher rank semi-simple groups. Zbl 1012.22022 Lubotzky, A.; Venkataramana, T. N. 2 2002 Tree lattices. With appendices by H. Bass, L. Carbone, A. Lubotzky, G. Rosenberg, and J. Tits. Zbl 1053.20026 Bass, Hyman; Lubotzky, Alexander 54 2001 Rank-1 phenomena for mapping class groups. Zbl 1025.20023 Farb, Benson; Lubotzky, Alexander; Minsky, Yair 35 2001 The product replacement algorithm and Kazhdan’s property (T). Zbl 0980.20078 Lubotzky, Alexander; Pak, Igor 32 2001 Pro-finite presentations. Zbl 0985.20017 Lubotzky, Alexander 27 2001 Enumerating boundedly generated finite groups. Zbl 1052.20017 Lubotzky, Alexander 12 2001 Arithmetic structure of fundamental groups and actions of semisimple Lie groups. Zbl 0985.22005 Lubotzky, Alexander; Zimmer, Robert J. 5 2001 ...and 62 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,605 Authors 89 Lubotzky, Alexander 50 Shalev, Aner 33 Lucchini, Andrea 27 Guralnick, Robert Michael 25 Shumyatsky, Pavel 23 Liebeck, Martin Walter 20 Kassabov, Martin D. 19 Klopsch, Benjamin 19 Pyber, László 18 Alon, Noga 18 Jaikin-Zapirain, Andrei 18 Kaufman, Tali 18 Larsen, Michael Jeffrey 18 Zalesskii, Pavel 16 Bridson, Martin R. 16 Gelander, Tsachik 14 Linial, Nathan 14 Wigderson, Avi 13 Gamburd, Alexander 13 Kantor, William M. 13 Khukhro, Evgeniĭ I. 13 Mann, Avinoam 13 Segal, Daniel 12 Abért, Miklós 12 Belolipetsky, Mikhail V. 12 Bou-Rabee, Khalid 12 Bourgain, Jean 12 Rapinchuk, Andrei S. 11 Avni, Nir 11 Koberda, Thomas 11 Magid, Andy Roy 11 Reid, Alan W. 10 Ershov, Mikhail V. 10 Grunewald, Fritz J. 10 Leuzinger, Enrico 10 Margalit, Dan 10 Meiri, Chen 10 Moravec, Primož 10 Mozes, Shahar 10 Parzanchevski, Ori 10 Porti, Joan 10 Salehi Golsefidy, Alireza 10 Sarnak, Peter Clive 10 Thom, Andreas Berthold 9 Acciarri, Cristina 9 Bekka, Mohammed el Bachir 9 Capdeboscq, Inna 9 Caprace, Pierre-Emmanuel 9 Detomi, Eloisa 9 Lackenby, Marc 9 Meshulam, Roy 9 Müller, Thomas W. 9 Nikolov, Nikolay Valeriev 9 Shusterman, Mark 9 Vdovina, Alina A. 9 Voll, Christopher 8 Azarov, Dmitriĭ Nikolaevich 8 Detinko, Alla S. 8 Dinur, Irit 8 Glasner, Yair 8 Golubev, Konstantin 8 Haran, Dan 8 Heusener, Michael 8 Jarden, Moshe 8 Kunyavskiĭ, Boris Èmmanuilovich 8 Leedham-Green, Charles R. 8 Levit, Arie 8 Lim, Seonhee 8 Long, Darren D. 8 Mason, Alexander W. 8 McReynolds, David Ben 8 Mohar, Bojan 8 Myasnikov, Alexei G. 8 Oppenheim, Izhar 8 Ozawa, Narutaka 8 Sikora, Adam S. 8 Tiep Pham Huu 8 Tran, Anh Tuan 8 Wong, Kok Bin 7 Aramayona, Javier 7 Babai, László 7 Bader, Uri 7 Breuillard, Emmanuel 7 Carbone, Lisa J. 7 Cioabă, Sebastian M. 7 Conder, Marston Donald Edward 7 de Cornulier, Yves 7 Flannery, Dane Laurence 7 Goldman, William M. 7 González-Meneses, Juan 7 González-Sánchez, Jon 7 Gorodnik, Alexander 7 Grigorchuk, Rostislav Ivanovich 7 Ioana, Adrian 7 Kapovich, Michael 7 Kionke, Steffen 7 Ku, Cheng Yeaw 7 Nevo, Amos 7 O’Brien, Eamonn A. 7 Pak, Igor ...and 2,505 more Authors all top 5 Cited in 346 Serials 197 Journal of Algebra 149 Israel Journal of Mathematics 84 Transactions of the American Mathematical Society 69 Proceedings of the American Mathematical Society 63 Advances in Mathematics 57 Geometriae Dedicata 48 Journal of Group Theory 47 Groups, Geometry, and Dynamics 46 Inventiones Mathematicae 44 Duke Mathematical Journal 39 International Journal of Algebra and Computation 37 Mathematische Zeitschrift 37 Algebraic & Geometric Topology 36 Communications in Algebra 35 Journal of Pure and Applied Algebra 35 Geometry & Topology 33 Mathematische Annalen 33 Combinatorica 31 Geometric and Functional Analysis. 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Quatrième Série 8 Commentarii Mathematici Helvetici 8 The Journal of Symbolic Logic 8 Mathematische Nachrichten 8 SIAM Journal on Computing 8 Computational Complexity 8 International Journal of Group Theory 7 Information Processing Letters 7 Linear and Multilinear Algebra 7 Mathematics of Computation 7 Manuscripta Mathematica 7 Memoirs of the American Mathematical Society 7 Journal of Knot Theory and its Ramifications 7 Oberwolfach Reports 7 Algebra & Number Theory 6 Journal d’Analyse Mathématique 6 Journal of Combinatorial Theory. Series A 6 Journal of Computer and System Sciences 6 Designs, Codes and Cryptography 6 Journal of Algebra and its Applications 6 Journal of Noncommutative Geometry 6 Groups, Complexity, Cryptology 6 European Journal of Mathematics 5 Mathematical Notes 5 Algebra and Logic 5 Bulletin de la Société Mathématique de France 5 Illinois Journal of Mathematics 5 Indiana University Mathematics Journal 5 Journal of Computational and Applied Mathematics 5 Journal of Complexity ...and 246 more Serials all top 5 Cited in 55 Fields 1,451 Group theory and generalizations (20-XX) 660 Combinatorics (05-XX) 387 Number theory (11-XX) 380 Manifolds and cell complexes (57-XX) 376 Topological groups, Lie groups (22-XX) 233 Computer science (68-XX) 178 Algebraic geometry (14-XX) 141 Dynamical systems and ergodic theory (37-XX) 124 Probability theory and stochastic processes (60-XX) 105 Functional analysis (46-XX) 88 Differential geometry (53-XX) 84 Information and communication theory, circuits (94-XX) 62 Geometry (51-XX) 61 Global analysis, analysis on manifolds (58-XX) 58 Functions of a complex variable (30-XX) 57 Mathematical logic and foundations (03-XX) 57 Nonassociative rings and algebras (17-XX) 56 Linear and multilinear algebra; matrix theory (15-XX) 55 Associative rings and algebras (16-XX) 53 Algebraic topology (55-XX) 52 Field theory and polynomials (12-XX) 51 Quantum theory (81-XX) 46 Abstract harmonic analysis (43-XX) 43 Several complex variables and analytic spaces (32-XX) 33 \(K\)-theory (19-XX) 28 Convex and discrete geometry (52-XX) 26 Operator theory (47-XX) 26 Operations research, mathematical programming (90-XX) 24 Measure and integration (28-XX) 18 Commutative algebra (13-XX) 17 Numerical analysis (65-XX) 16 Ordinary differential equations (34-XX) 16 General topology (54-XX) 16 Statistical mechanics, structure of matter (82-XX) 14 General and overarching topics; collections (00-XX) 14 Partial differential equations (35-XX) 10 Order, lattices, ordered algebraic structures (06-XX) 10 Statistics (62-XX) 9 Potential theory (31-XX) 7 Category theory; homological algebra (18-XX) 7 Difference and functional equations (39-XX) 7 Approximations and expansions (41-XX) 6 History and biography (01-XX) 5 Special functions (33-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Mechanics of particles and systems (70-XX) 4 Relativity and gravitational theory (83-XX) 4 Biology and other natural sciences (92-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 General algebraic systems (08-XX) 2 Real functions (26-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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