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Commentarii Mathematici Helvetici, ISSN 0010-2571, 2019, Volume 94, Issue 1, p. 53
Journal Article
1994, Progress in mathematics, ISBN 9780817650759, Volume 125., xi, 195
Book
2003, Progress in mathematics, ISBN 0817669892, Volume 212., xxii, 453
Book
03/1952, 458
Book
Japanese Journal of Mathematics, ISSN 0289-2316, 9/2014, Volume 9, Issue 2, pp. 137 - 169
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 01/2020, Volume 278, Issue 1, p. 108298
In recent years, there has been a considerable amount of interest in the stability of a finitely-generated group Γ with respect to a sequence of groups ,... 
Group theoretic stability | Property (T)
Journal Article
ISRAEL JOURNAL OF MATHEMATICS, ISSN 0021-2172, 08/2019, Volume 232, Issue 1, pp. 201 - 229
In [BGLM] and [GLNP] it was conjectured that if H is a simple Lie group of real rank at least 2, then the number of conjugacy classes of (arithmetic) lattices... 
ALGEBRAIC-GROUPS | EXISTENCE | MATHEMATICS | NUMBER | SUBGROUP GROWTH | Mathematical research | Lattice theory | Research
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 08/2014, Volume 55, Issue 8, pp. 82202 - 273
Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are low density parity check codes... 
BETTI NUMBER | SURFACE | PHYSICS, MATHEMATICAL | Error correcting codes | Error correction | Mathematics - Differential Geometry | FOUR-DIMENSIONAL CALCULATIONS | PARITY | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | COMPUTER CODES | MATHEMATICAL MANIFOLDS | MATHEMATICAL METHODS AND COMPUTING | GEOMETRY | GRAPH THEORY
Journal Article
Glasgow Mathematical Journal, ISSN 0017-0895, 2014, Volume 56, Issue 2, pp. 465 - 469
In response to questions by Kassabov, Nikolov and Shalev, we show that a given subset A of a finite simple group G is the image of some word map w : G x G. G... 
MATHEMATICS | Mathematics | Maps | Mathematical analysis | Invariants | Group theory | Images
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 02/2014, Volume 46, Issue 1, pp. 103 - 110
In this note, we show that various (geometric/homological) finiteness properties are not profinite properties. For example, for all positive integers k and ℓ,... 
MATHEMATICS | REPRESENTATIONS | ARITHMETIC GROUPS
Journal Article
Journal of Autism and Developmental Disorders, ISSN 0162-3257, 3/2019, Volume 49, Issue 3, pp. 1284 - 1288
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 7/2019, Volume 217, Issue 1, pp. 219 - 240
If $$\Gamma $$ Γ is an irreducible non-uniform higher-rank characteristic zero arithmetic lattice (for example $${{\,\mathrm{SL}\,}}_n({\mathbb {Z}})$$ SL n (... 
Mathematics, general | Mathematics | Arithmetic
Journal Article
Bulletin of Mathematical Sciences, ISSN 1664-3607, 04/2019, p. 1950016
We show that for a fixed [Formula: see text], Gromov random groups with any density [Formula: see text] have no nontrivial degree [Formula: see text]... 
Journal Article
2010, Modern Birkhũser Classics, ISBN 3034603312
The book presents the solutions to two problems: the first is the construction of expanding graphs – graphs which are of fundamental importance for... 
Global differential geometry | Group theory | Mathematics | Number theory
Web Resource
Journal of the European Mathematical Society, ISSN 1435-9855, 2011, Volume 13, Issue 5, pp. 1331 - 1341
We prove that all finite simple groups of Lie type, with the exception of the Suzuki groups, can be made into a family of expanders in a uniform way. This... 
MATHEMATICS | EXPLICIT CONSTRUCTIONS | MATHEMATICS, APPLIED | SUBGROUPS | RAMANUJAN COMPLEXES | GRAPHS
Journal Article
DUKE MATHEMATICAL JOURNAL, ISSN 0012-7094, 09/2019, Volume 168, Issue 12, pp. 2207 - 2234
Consider Sym(n) endowed with the normalized Hamming metric d(n). A finitely generated group F is P-stable if every almost homomorphism rho(nk) : Gamma ->... 
MATHEMATICS | EVERY PROPERTY | HYPERFINITE GRAPHS
Journal Article
Journal of the American Mathematical Society, ISSN 0894-0347, 2012, Volume 25, Issue 4, pp. 1119 - 1148
A general sieve method for groups is formulated. It enables one to ``measure'' subsets of a finitely generated group. As an application we show that if \Gamma... 
Homomorphisms | Prime numbers | Arithmetic progressions | Mathematical theorems | Random walk | Group theory | Eigenvalues | Automorphisms | Vertices | Powers | Finite groups of Lie type | Property-t | Sieve | Linear groups | MATHEMATICS | linear groups | RANDOM-WALKS | property-tau | EXPANSION | GROWTH | SUBGROUPS | powers | finite groups of Lie type | EXPANDER GRAPHS
Journal Article
Advances in Mathematics, ISSN 0001-8708, 02/2015, Volume 272, pp. 743 - 760
Expander graphs have been playing an important role in combinatorics and computer science over the last four decades. In recent years a theory of high... 
Random complexes | Expansion | Simplicial complexes | 55U10 | 68Q87 | MATHEMATICS | COMPLEXES | HOMOLOGICAL CONNECTIVITY | GRAPHS | Computer science | Analysis
Journal Article
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