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Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras. It is interesting to see the remarkable advances that have been made in operator algebras over these years, which strikingly illustrate the vitality of the field. A total of 26 talks were given at the symposium on a variety of themes, all highlighting the richness of the subject. The field of operator algebras was created in the 1930s and was motivated by problems of quantum mechanics. It has subsequently developed well beyond its initial intended realm of applications and expanded into such diverse areas of mathematics as representation theory, dynamical systems, differential geometry, number theory and quantum algebra. One branch, known as “noncommutative geometry”, has become a powerful tool for studying phenomena that are beyond the reach of classical analysis. This volume includes research papers that present new results, surveys that discuss the development of a specific line of research, and articles that offer a combination of survey and research. These contributions provide a multifaceted portrait of beautiful mathematics that both newcomers to the field of operator algebras and seasoned researchers alike will appreciate.
Mathematics. --- K-theory. --- Dynamics. --- Ergodic theory. --- Functional analysis. --- Mathematical physics. --- Functional Analysis. --- Dynamical Systems and Ergodic Theory. --- K-Theory. --- Mathematical Physics. --- Operator algebras --- Differentiable dynamical systems. --- Algebraic topology --- Homology theory --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Physical mathematics --- Physics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics
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Based on presentations given at the NordForsk Network Closing Conference “Operator Algebra and Dynamics,” held in Gjáargarður, Faroe Islands, in May 2012, this book features high quality research contributions and review articles by researchers associated with the NordForsk network and leading experts that explore the fundamental role of operator algebras and dynamical systems in mathematics with possible applications to physics, engineering and computer science. It covers the following topics: von Neumann algebras arising from discrete measured groupoids, purely infinite Cuntz-Krieger algebras, filtered K-theory over finite topological spaces, C*-algebras associated to shift spaces (or subshifts), graph C*-algebras, irrational extended rotation algebras that are shown to be C*-alloys, free probability, renewal systems, the Grothendieck Theorem for jointly completely bounded bilinear forms on C*-algebras, Cuntz-Li algebras associated with the a-adic numbers, crossed products of injective endomorphisms (the so-called Stacey crossed products), the interplay between dynamical systems, operator algebras and wavelets on fractals, C*-completions of the Hecke algebra of a Hecke pair, semiprojective C*-algebras, and the topological dimension of type I C*-algebras. Operator Algebra and Dynamics will serve as a useful resource for a broad spectrum of researchers and students in mathematics, physics, and engineering.
Mathematics --- Group theory --- Algebra --- Differential geometry. Global analysis --- Topological groups. Lie groups --- Functional analysis --- Harmonic analysis. Fourier analysis --- Ergodic theory. Information theory --- Mathematical analysis --- legeringen --- algebra --- analyse (wiskunde) --- topologie (wiskunde) --- differentiaal geometrie --- Fourierreeksen --- functies (wiskunde) --- mathematische modellen --- wiskunde --- informatietheorie
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Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras. It is interesting to see the remarkable advances that have been made in operator algebras over these years, which strikingly illustrate the vitality of the field. A total of 26 talks were given at the symposium on a variety of themes, all highlighting the richness of the subject. The field of operator algebras was created in the 1930s and was motivated by problems of quantum mechanics. It has subsequently developed well beyond its initial intended realm of applications and expanded into such diverse areas of mathematics as representation theory, dynamical systems, differential geometry, number theory and quantum algebra. One branch, known as “noncommutative geometry”, has become a powerful tool for studying phenomena that are beyond the reach of classical analysis. This volume includes research papers that present new results, surveys that discuss the development of a specific line of research, and articles that offer a combination of survey and research. These contributions provide a multifaceted portrait of beautiful mathematics that both newcomers to the field of operator algebras and seasoned researchers alike will appreciate.
Functional analysis --- Ergodic theory. Information theory --- Mathematics --- Mathematical physics --- Classical mechanics. Field theory --- Physics --- functies (wiskunde) --- zeevaartagenten --- wiskunde --- fysica --- dynamica --- informatietheorie
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Based on presentations given at the NordForsk Network Closing Conference “Operator Algebra and Dynamics,” held in Gjáargarður, Faroe Islands, in May 2012, this book features high quality research contributions and review articles by researchers associated with the NordForsk network and leading experts that explore the fundamental role of operator algebras and dynamical systems in mathematics with possible applications to physics, engineering and computer science. It covers the following topics: von Neumann algebras arising from discrete measured groupoids, purely infinite Cuntz-Krieger algebras, filtered K-theory over finite topological spaces, C*-algebras associated to shift spaces (or subshifts), graph C*-algebras, irrational extended rotation algebras that are shown to be C*-alloys, free probability, renewal systems, the Grothendieck Theorem for jointly completely bounded bilinear forms on C*-algebras, Cuntz-Li algebras associated with the a-adic numbers, crossed products of injective endomorphisms (the so-called Stacey crossed products), the interplay between dynamical systems, operator algebras and wavelets on fractals, C*-completions of the Hecke algebra of a Hecke pair, semiprojective C*-algebras, and the topological dimension of type I C*-algebras. Operator Algebra and Dynamics will serve as a useful resource for a broad spectrum of researchers and students in mathematics, physics, and engineering.
Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Mathematical analysis. --- Algebra. --- 517.1 Mathematical analysis --- Mathematical analysis --- Mathematics. --- Associative rings. --- Rings (Algebra). --- Group theory. --- Topological groups. --- Lie groups. --- Harmonic analysis. --- Dynamics. --- Ergodic theory. --- Functional analysis. --- Abstract Harmonic Analysis. --- Associative Rings and Algebras. --- Dynamical Systems and Ergodic Theory. --- Functional Analysis. --- Group Theory and Generalizations. --- Topological Groups, Lie Groups. --- Mathematics --- Differentiable dynamical systems. --- Topological Groups. --- Groups, Topological --- Continuous groups --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Ergodic transformations --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Operator algebras --- Differentiable dynamical systems
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