“…In recent years, newly developed techniques from algebraic geometry and combinatorics have been applied with great success to some of the outstanding problems of invariant theory, moving it back to the forefront of mathematical research once again. …”
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“…A research monograph in algebraic geometry, it addresses researchers and graduate students.…”
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“…Math.133 (1991) and together give an approach to the proof that is accessible to Ph.D-level students in number theory and algebraic geometry. Each chapter is based on an instructional lecture given by its author ata special conference for graduate students, on the topic of Faltings' paper.…”
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“…It is of interest to graduate students and researchers who work in algebraic geometry (not only real) and have some familiarity with the basics of étale cohomology and Grothendieck sites. …”
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“…These notes are highly selfcontained and should be accessible to any graduate student in commutative algebra or algebraic geometry. They include fully self-contained presentations of the theorems of Ferrand-Szpiro, Cowsik-Nori and the techniques of Lindel.…”
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“…Categorical algebra and its applications contain several fundamental papers on general category theory, by the top specialists in the field, and many interesting papers on the applications of category theory in functional analysis, algebraic topology, algebraic geometry, general topology, ring theory, cohomology, differential geometry, group theory, mathematical logic and computer sciences. …”
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“…In the Teichmüller theory of Riemann surfaces, besides the classical theory of quasi-conformal mappings, vari- ous approaches from differential geometry and algebraic geometry have merged in recent years. Thus the central subject of "Complex Structure" was a timely choice for the joint meetings in Katata and Kyoto in 1989. …”
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“…This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. …”
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“…His own contribution then develops connections with algebraic geometry, and inclu…”
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“…Poncelet's theorem is a famous result in algebraic geometry, dating to the early part of the nineteenth century. …”
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“…A rigorous introduction to basic number theory, rings, fields, polynomial theory, groups, algebraic geometry and elliptic curves prepares students for exploring their practical applications related to storing, securing, retrieving and communicating information in the electronic world. …”
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“…Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric v…”
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“…This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. …”
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“…The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinit…”
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“…It is by now a well-known paradigm that public-key cryptosystems can be built using finite Abelian groups and that algebraic geometry provides a supply of such groups through Abelian varieties over finite fields. …”
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“…This book presents a systematic approach to conformal field theory with gauge symmetry from the point of view of complex algebraic geometry. After presenting the basic facts of the theory of compact Riemann surfaces and the representation theory of affine Lie algebras in Chapters 1 and 2, conformal blocks for pointed Riemann surfaces with coordinates are constructed in Chapter 3. …”
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“…Lefschetz takes the opportunity to describe some of the important applications of his theory, particularly in algebraic geometry, to problems such as counting intersections of …”
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“…This volume covers four important areas in coding theory: algebraic geometry codes, graph-based codes, space-time codes, and quantum codes. …”
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“…It is intended to serve as an introduction to the topical question of classification of holomorphic vector bundles on complex projective spaces, and can easily be read by students with a basic knowledge of analytic or algebraic geometry. Short supplementary sections describe more advanced topics, further results, and unsolved problems.…”
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“…Theta series for lattices with indefinite signature $(n_+,n_-)$ arise in many areas of mathematics including representation theory and enumerative algebraic geometry. Their modular properties are well understood in the Lorentzian case ($n_+=1$), but have remained obscure when $n_+\geq 2$. …”
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