“…The theory of commutative fields is a fundamental area of mathematics, particularly in number theory, algebra, and algebraic geometry. However, few books provide sufficient treatment of this topic. …”
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“…This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. …”
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“…The book is an important source of information for specialists in algebraic geometry and its application to mathematical aspects of quantum field theory.…”
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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. …”
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“…The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.…”
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“…The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In particular, Thue equations, norm form equations and S-unit equations, with emphasis on recent explicit bounds on the number of solutions, are included. …”
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“…The book is essentially self-contained, assuming only a basic knowledge of algebraic geometry; it is intended both for graduate students and research mathematicians interested in Hilbert schemes, enumertive geometry and moduli spaces.…”
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“…The reader is expected to have a sound background in algebraic geometry. Large parts of the book are expository, and intended as a reference for the working mathematician. …”
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“…Except for this last item, which requires more substantial background in algebraic geometry and especially abelian varieties, the rest of the book is basically elementary, depending only on standard homological algebra at the level of first year graduate students.…”
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“…Papers in the volume cover a wide spectrum of number theoretic topics ranging from additive number theory and diophantine approximations to algebraic number theory and relations with algebraic geometry and topology.…”
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“…Over the past 2O years classical Hodge theory has undergone several generalizations of great interest in algebraic geometry. The papers in this volume reflect the recent developments in the areas of: mixed Hodge theory on the cohomology of singular and open varieties, on the rational homotopy of algebraic varieties, on the cohomology of a link, and on the vanishing cycles; L -realization of the intersection cohomology for the cases of singular varieties and smooth varieties with degenerating coefficients; applications of cubical hyperresolutions and of iterated integrals; asymptotic behavior of degenerating variations of Hodge structure; the geometric realization of maximal variations; and variations of mixed Hodge structure. …”
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“…The goal of the symposium was to bring together mathematicians whose research efforts have led to recent advances in algebraic geometry, algebraic K-theory, algebraic topology, and mathematical physics. …”
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“…All research articles were written by leading experts, some of whom are prize winners in the fields of complex geometry, algebraic geometry and analysis. The book offers a valuable resource for all researchers interested in recent developments in analysis and geometry.…”
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“…These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. …”
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“…We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology.…”
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“…Then, we give several example of applications, in particular matrix models, enumeration of discrete surfaces (maps), algebraic geometry and topological strings, non-intersecting brownian motions,...…”
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“…Then, we give several examples of applications, in particular matrix models, enumeration of discrete surfaces (maps), algebraic geometry and topological strings, and non-intersecting Brownian motions.…”
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“…Grothendieck's duality theory for coherent cohomology is a fundamental tool in algebraic geometry and number theory, in areas ranging from the moduli of curves to the arithmetic theory of modular forms. …”
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“…The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory and applications in the sciences. …”
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“…Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. …”
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