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Expander graphs in pure and applied mathematics (Q3109810)

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Language	Label	Description	Also known as
English	Expander graphs in pure and applied mathematics	scientific article

Statements

scholarly article

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Expander graphs in pure and applied mathematics (English)

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zbMATH Open document ID

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10.1090/S0273-0979-2011-01359-3

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Alexander Lubotzky

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Bulletin of the American Mathematical Society

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publication date

26 January 2012

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full work available at URL

https://arxiv.org/abs/1105.2389

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Mathematics Subject Classification ID

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zbMATH DE Number

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zbMATH Keywords

expander graphs

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sparse finite graphs

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MaRDI profile type

MaRDI publication profile

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The rank gradient from a combinatorial viewpoint.

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Rank gradient, cost of groups and the rank versus Heegaard genus problem

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Explicit construction of linear sized tolerant networks

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Small-diameter Cayley graphs for finite simple groups

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On amenability of group algebras. I.

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Statistical properties of subgroups of free groups

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On the full C*-algebras of arithmetic groups and the congruence subgroup problem

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Expanders and dimensional expansion

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A proof of the positive density conjecture for integer Apollonian circle packings

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Invariant measures and stiffness for non-Abelian groups of toral automorphisms

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Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\).

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On the spectral gap for finitely-generated subgroups of \(\text{SU}(2)\)

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Expansion and random walks in \(\text{SL}_d(\mathbb{Z}/p^n\mathbb{Z})\). I.

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Expansion and random walks in \(\text{SL}_d(\mathbb{Z}/p^n\mathbb{Z})\). II.

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Sieving and expanders

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Affine linear sieve, expanders, and sum-product

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Generalization of Selberg's \(\frac {3}{16} \) theorem and affine sieve

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A sum-product estimate in finite fields, and applications

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On representations of integers in thin subgroups of \(\text{SL}_2(\mathbb Z)\)

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On conjugacy growth of linear groups

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Strong uniform expansion in \(\text{SL}(2,p)\).

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Linear approximate groups.

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Approximate subgroups of linear groups.

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Suzuki groups as expanders.

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Strongly dense free subgroups of semisimple algebraic groups.

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Expansion in finite simple groups of Lie type.

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On Fibonacci numbers with few prime divisors

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Ramanujan duals. II

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Geometry and spectra of compact Riemann surfaces

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Generating random elements of a finite group

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Démonstration de la conjecture \(\tau\). (Proof of the \(\tau\)-conjecture.)

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Walks on generating sets of groups

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Growth in SL2 over finite fields

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The probability of generating the symmetric group

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Finite covers of random 3-manifolds

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Towards dimension expanders over finite fields

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The amenability of affine algebras

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Expander graphs, gonality, and variation of Galois representations

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Linnik's ergodic method and the distribution of integer points on spheres

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Golod-Shafarevich groups with property \((T)\) and Kac-Moody groups.

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Property \((T)\) for noncommutative universal lattices

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Overlap properties of geometric expanders

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A proof of Alon’s second eigenvalue conjecture and related problems

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Some Experiments with Integral Apollonian Circle Packings

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Cost of equivalence relations and groups

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On the spectral gap for infinite index ``congruence'' subgroups of SL\(_2(\mathbb{Z})\)

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On the girth of random Cayley graphs

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Spectra of elements in the group ring of SU(2)

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Growth of Small Generating Sets in SLn(Z/pZ)

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Quasirandom Groups

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Apollonian circle packings: Number theory

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The primes contain arbitrarily long arithmetic progressions

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Linear equations in primes

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An inverse theorem for the Gowers \(U^{s+1}[N]\)-norm

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Addendum to ``Random walk in random groups'' by M. Gromov.

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Singularities, expanders and topology of maps. I: Homology versus volume in the spaces of cycles

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Singularities, expanders and topology of maps. II: From combinatorics to topology via algebraic isoperimetry

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Generalizations of the Kolmogorov-Barzdin embedding estimates

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Linear representations of the automorphism group of a free group.

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Growth and generation in \(\text{SL}_2(\mathbb{Z}/p\mathbb{Z})\).

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Growth in \(\mathrm{SL}_3(\mathbb Z/p\mathbb Z)\).

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Counterexamples to the Baum-Connes conjecture

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Expander graphs and their applications

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Powers in Finitely Generated Groups

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Splitting fields of characteristic polynomials of random elements in arithmetic groups

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The probability of generating a finite classical group

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Invariable generation and the Chebotarev invariant of a finite group.

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Generic-case complexity, decision problems in group theory, and random walks.

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Average-case complexity and decision problems in group theory.

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On group-theoretic models of randomness and genericity.

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Universal lattices and unbounded rank expanders.

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Symmetric groups and expander graphs.

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Finite simple groups as expanders

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Universal lattices and property \(\tau\)

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Edge transitive ramanujan graphs and symmetric LDPC good codes

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Symmetric LDPC Codes and Local Testing

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Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂

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Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds

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Almost prime Pythagorean triples in thin orbits

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Amplification arguments for large sieve inequalities

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Expanders, rank and graphs of groups

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A characterisation of large finitely presented groups.

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Heegaard splittings, the virtually Haken conjecture and property \((\tau)\)

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Large groups, property (τ) and the homology growth of subgroups

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LERF and the Lubotzky-Sarnak conjecture

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Covering Spaces of Arithmetic 3-Orbifolds

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On the cost of generating an equivalence relation

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The probability of generating a finite simple group

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Heegaard genus and property τ for hyperbolic 3-manifolds

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Prym representations of mapping class groups

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Discrete groups, expanding graphs and invariant measures. With an appendix by Jonathan D. Rogawski

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Eigenvalues of the Laplacian, the first Betti number and the congruence subgroup problem

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Free quotients and the first Betti number of some hyperbolic manifolds

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Finite simple groups of Lie type as expanders.

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Sieve methods in group theory I: Powers in linear groups

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Sieve methods in group theory. II: The mapping class group

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The product replacement algorithm and Kazhdan’s property (T)

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Ramanujan graphs

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Hecke operators and distributing points on <i>S</i><sup>2</sup>. II

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The Galois group of random elements of linear groups

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Ramanujan complexes of type \(\widetilde A_d\)

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Explicit constructions of Ramanujan complexes of type \(\widetilde A_d\).

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Subgroup growth.

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Dimension expanders

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Variants of Kazhdan's property for subgroups of semisimple groups

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Random walks on the mapping class group

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Random Heegaard splittings

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On Genericity of Pseudo-Anosovs in the Torelli Group

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Explicit constructions of graphs without short cycles and low density codes

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Congruence Properties of Zariski-Dense Subgroups I

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Expanders in group algebras

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Existence and explicit constructions of \(q+1\) regular Ramanujan graphs for every prime power \(q\)

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Generic complexity of undecidable problems

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Prime and almost prime integral points on principal homogeneous spaces

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A product decomposition for the classical quasisimple groups

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Product decompositions of quasirandom groups and a Jordan type theorem.

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On subgroups of \(GL_ n(F_ p)\)

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Strong approximation for Zariski dense subgroups over arbitrary global fields

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Growth in finite simple groups of Lie type

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Entropy waves, the zig-zag graph product, and new constant-degree expanders

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Walks on groups, counting reducible matrices, polynomials, and surface and free group automorphisms

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Zariski Density and Genericity

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The affine sieve

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Expansion in perfect groups.

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Integral Apollonian Packings

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Sur certaines hypothèses concernant les nombres premiers

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Le problème des groupes de congruence pour \(SL_2\)

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Expanding graphs and invariant means

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Bounded generation and Kazhdan's property (T)

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A recursive approach to low complexity codes

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Free subgroups in linear groups

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An application of Ramanujan graphs to \(C^*\)-algebra tensor products

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Strong approximation for Zariski-dense subgroups of semi-simple algebraic groups

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A spectral proof of Rademacher's conjecture for congruence subgroups of the modular group.

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Property (T) and Kazhdan constants for discrete groups

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Mathematics(1 entry)

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