“…Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. …”
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“…Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. …”
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“…We use techniques from signal processing, optimization, and applied algebraic geometry to obtain theoretical and computational contributions for this challenging nonlinear inverse problem with sparsity constraints. …”
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“…Finally, using techniques from algebraic geometry, we prove that the minimal nontrivial interaction length n for any symmetric state is bounded by [Image: see text].…”
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“…Moreover, there are far-reaching mathematical ramifications that have led to a successful dialogue with differential and algebraic geometry. These lecture notes aim to introduce students of modern theoretical physics to the fascinating developments in the understanding of N=2 supersymmetric gauge theories in a coherent fashion. …”
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“…This volume reviews and updates a prominent series of workshops in representation/Lie theory, and reflects the widespread influence of those  workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, and mathematical physics.  Many of the contributors have had leading roles in both the classical and modern developments of Lie theory and its applications. …”
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“…One aspect of these actions, not surprising in itself but quite striking in its extent and depth nonetheless, is the connection with commutative algebra and arithmetical algebraic geometry. The algebraic framework resulting from this connection allows the construction of examples with a variety of specified dynamical properties, and by combining algebraic and dynamical tools one obtains a quite detailed understanding of this class of Zd-actions. ----------------------- It is a marvelous display of the richness and depth of the interplay between dynamical systems on one hand and commutative algebra and number theory on the other. (...) …”
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“…This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. …”
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“…Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. …”
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“…These structures find their motivation in a wide range of fields, from algebraic topology to mathematical physics, algebraic geometry and mathematical logic. While strict $n$-categories are easily defined in terms associative and unital composition operations they are of limited use in applications, which often call for weakened variants of these laws. …”
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“…Assuming basic knowledge of algebraic geometry and algebraic number theory, the book is almost self-contained. …”
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“…At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. …”
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“…In this paper we use algebraic geometry to formally model 2-dimensional acoustic target tracking and then prove its best degree of required sensing coverage. …”
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“…By introducing algebraic geometry to citation studies, we add a new tool to existing methods for the analysis of content-related social influences.…”
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“…Motivated by the recent realization of hyperbolic lattices in circuit quantum electrodynamics, we exploit ideas from algebraic geometry to construct a hyperbolic generalization of Bloch theory, despite the absence of commutative translation symmetries. …”
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“…If one wants to expand on the usual algebraic geometry over a non-algebraically closed base field, e.g. a real closed field or p-adically closed field, one typically meets lots of valuation domains. …”
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“…Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. …”
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“…The first three parts are written in a self-contained manner and could be accessible to graduate students with a background in algebraic geometry and homotopy theory. It is designed to be a reference work and could also be useful outside motivic homotopy theory. …”
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“…Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. …”
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“…Starting from Lie's theory of local analytic transformation groups and early work on Lie algebras, he follows the process of globalization in its two main frameworks: differential geometry and topology on one hand, algebraic geometry on the other. Chapters II to IV are devoted to the former, Chapters V to VIII, to the latter. …”
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