“…Some familiarity with the usualminimax theory and basic algebraic topology is assumed.…”
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“…The theory originated in the early 1970s in homotopy theory and quickly became very important in algebraic topology, algebra, algebraic geometry, and even theoretical physics (string theory). …”
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“…The first one reviews the material from algebraic topology and Lie group theory needed for the comparison theorem. …”
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“…Within the theme of the workshop, the collected articles cover a broad range of topics and explore exciting new links between algebraic geometry, representation theory, group theory, number theory and algebraic topology. The book combines research and overview articles by prominent international researchers and provides a valuable resource for researchers and students alike. .…”
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“…The I*-measure is shown to differ from other homology and homotopy measures in that it is calculable with respect to most of the important geometric constructions encountered in algebraic topology. This approach provides a new method of treatment and leads to various new results. …”
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“…Topologists who desire to perform algebraic topology computations will appreciate the algorithmic potential of boolean representable complexes.…”
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“…It touches upon trendsetting areas such as Compressed Sensing, Finite Frames, Parametric Partial Differential Equations, Quantization, Finite Rate of Innovation, System Theory, as well as sampling in Geometry and Algebraic Topology.…”
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“…In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. …”
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“…It also has ties to other areas, including combinatorics, algebraic geometry, algebraic topology, commutative algebra and representation theory. …”
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“…Hyperplane Arrangements will be particularly useful to graduate students and researchers who are interested in algebraic geometry or algebraic topology. The book contains numerous exercises at the end of each chapter, making it suitable for courses as well as self-study.…”
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“…The primary physical models targeted are general relativity, spinors, and gauge theories, with notable chapters on Riemannian geometry, Clifford algebras, and fiber bundles.Contents: Mathematical Structures Abstract Algebra Vector Algebras Topological Spaces Algebraic Topology Manifolds Lie Groups Clifford Groups Riemannian Manifolds Fiber Bundles Categories and Functors  Readership: Students in mathematics and physics who want to explore a level deeper into actual mathematical content.…”
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“…Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. For some of the later chapters, it would be helpful to have some background on representation theory and complex geometry.…”
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“…Major topics covered include chains and antichains, lowest upper and greatest lower bounds, retractions, algorithmic approaches, lattices, the dimension of ordered sets, interval orders, lexicographic sums, products, enumeration, and the role of algebraic topology. This new edition shifts the primary focus to finite ordered sets, with results on infinite ordered sets presented toward the end of each chapter whenever possible. …”
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“…The body of the book consists of four chapters devoted to algebraic topology, Cech-Stone compactification, dimension theory and differential geometry. …”
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“…The book is appropriate for a course in discrete Morse theory, a supplemental text to a course in algebraic topology or topological combinatorics, or an independent study.…”
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“…Good knowledge of algebraic topology - both homotopy and homology theory - is assumed. …”
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“…With one exception, these papers are original and fully refereed research articles on various applications of Category Theory to Algebraic Topology, Logic and Computer Science. The exception is an outstanding and lengthy survey paper by Joyal/Street (80 pp) on a growing subject: it gives an account of classical Tannaka duality in such a way as to be accessible to the general mathematical reader, and to provide a key for entry to more recent developments and quantum groups. …”
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“…This book is ideal for self-study for mathematicians and students interested in such areas of geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. …”
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“…In the last decades, the prosperous interaction, built upon the joint efforts from both mathematicians and physicists, has given rise to marvelous deep results in supersymmetric gauge theory, topological string, M-theory and duality on the physics side as well as in algebraic geometry, differential geometry, algebraic topology, representation theory and number theory on the mathematics side. …”
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“…Using methods of algebraic topology and the maximal entropy principle, we demonstrate that gamma modulation synchronizes the spiking of dynamical cell assemblies, which enables learning a spatial map at faster timescales.…”
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