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This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics— such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. The ideas of higher homotopies and algebraic deformation have a growing number of theoretical applications and have played a prominent role in recent mathematical advances. For example, algebraic versions of higher homotopies have led eventually to the proof of the formality conjecture and the deformation quantization of Poisson manifolds. As observed in deformations and deformation philosophy, a basic observation is that higher homotopy structures behave much better than strict structures. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. Higher Structures in Geometry and Physics is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures. Contributors: L. Breen, A.S. Cattaneo, M. Cahen, V.A. Dolgushev, G. Felder, A. Giaquinto, S. Gutt, J. Huebschmann, T. Kadeishvili, H. Kajiura, B. Keller, Y. Kosmann-Schwarzbach, J.-L. Loday, S.A. Merkulov, D. Sternheimer, D.E. Tamarkin, C. Torossian, B.L. Tsygan, S. Waldmann, R.N. Umble.

Geometric quantization. --- Geometry, Algebraic -- Congresses. --- Homotopy theory -- Congresses. --- Ordered algebraic structures -- Congresses. --- Geometric quantization --- Mathematical physics --- Mathematics --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Algebra --- Calculus --- Geometry, Algebraic. --- Topological groups. --- Mathematical physics. --- Physical mathematics --- Groups, Topological --- Algebraic geometry --- Mathematics. --- Algebraic geometry. --- Group theory. --- Lie groups. --- Applied mathematics. --- Engineering mathematics. --- Physics. --- Topological Groups, Lie Groups. --- Group Theory and Generalizations. --- Algebraic Geometry. --- Mathematical Methods in Physics. --- Applications of Mathematics. --- Continuous groups --- Geometry --- Topological Groups. --- Geometry, algebraic. --- Math --- Science --- Groups, Theory of --- Substitutions (Mathematics) --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Engineering --- Engineering analysis --- Mathematical analysis

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Cognition in old age --- Intergenerational relations --- Older people --- Older people --- Economic aspects --- Finance, Personal. --- Nutrition

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This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. The ideas of higher homotopies and algebraic deformation have a growing number of theoretical applications and have played a prominent role in recent mathematical advances. For example, algebraic versions of higher homotopies have led eventually to the proof of the formality conjecture and the deformation quantization of Poisson manifolds. As observed in deformations and deformation philosophy, a basic observation is that higher homotopy structures behave much better than strict structures. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. Higher Structures in Geometry and Physics is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures. Contributors: L. Breen, A.S. Cattaneo, M. Cahen, V.A. Dolgushev, G. Felder, A. Giaquinto, S. Gutt, J. Huebschmann, T. Kadeishvili, H. Kajiura, B. Keller, Y. Kosmann-Schwarzbach, J.-L. Loday, S.A. Merkulov, D. Sternheimer, D.E. Tamarkin, C. Torossian, B.L. Tsygan, S. Waldmann, R.N. Umble.

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