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A1 Algebraic Topology over a Field

A1 Algebraic Topology over a Field Author Fabien Morel
ISBN-10 9783642295140
Release 2012-07-13
Pages 259
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This text deals with A1-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A1-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A1-homotopy sheaves, A1-homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.

Surveys on Recent Developments in Algebraic Geometry

Surveys on Recent Developments in Algebraic Geometry Author Izzet Coskun
ISBN-10 9781470435578
Release 2017-07-12
Pages 370
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The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.

Quandles and Topological Pairs

Quandles and Topological Pairs Author Takefumi Nosaka
ISBN-10 9789811067938
Release 2017-11-20
Pages 136
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This book surveys quandle theory, starting from basic motivations and going on to introduce recent developments of quandles with topological applications and related topics. The book is written from topological aspects, but it illustrates how esteemed quandle theory is in mathematics, and it constitutes a crash course for studying quandles.More precisely, this work emphasizes the fresh perspective that quandle theory can be useful for the study of low-dimensional topology (e.g., knot theory) and relative objects with symmetry. The direction of research is summarized as “We shall thoroughly (re)interpret the previous studies of relative symmetry in terms of the quandle”. The perspectives contained herein can be summarized by the following topics. The first is on relative objects G/H, where G and H are groups, e.g., polyhedrons, reflection, and symmetric spaces. Next, central extensions of groups are discussed, e.g., spin structures, K2 groups, and some geometric anomalies. The third topic is a method to study relative information on a 3-dimensional manifold with a boundary, e.g., knot theory, relative cup products, and relative group cohomology.For applications in topology, it is shown that from the perspective that some existing results in topology can be recovered from some quandles, a method is provided to diagrammatically compute some “relative homology”. (Such classes since have been considered to be uncomputable and speculative). Furthermore, the book provides a perspective that unifies some previous studies of quandles.The former part of the book explains motivations for studying quandles and discusses basic properties of quandles. The latter focuses on low-dimensional topology or knot theory. Finally, problems and possibilities for future developments of quandle theory are posed.

A Singular Introduction to Commutative Algebra

A Singular Introduction to Commutative Algebra Author Gert-Martin Greuel
ISBN-10 9783662049631
Release 2012-12-06
Pages 588
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This book can be understood as a model for teaching commutative algebra, and takes into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, the authors show how the concept can be worked on using a computer. The computations are exemplified with the computer algebra system Singular, developed by the authors. Singular is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry. The book includes a CD containing Singular as well as the examples and procedures explained in the book.

Mathematical Methods in Economics and Social Choice

Mathematical Methods in Economics and Social Choice Author norman schofield
ISBN-10 3540211381
Release 2004-03-15
Pages 300
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In recent years, the usual optimisation techniques have been extended to incorporate more powerful topological and differential methods, and these methods have led to new results on the qualitative behaviour of general economic and political systems. The progression of ideas presented in this book will familiarize the student with the geometric concepts underlying these topological methods, and, as a result, make mathematical economics, general equilibrium theory, and social choice theory more accessible.

Foundations of Grothendieck Duality for Diagrams of Schemes

Foundations of Grothendieck Duality for Diagrams of Schemes Author Joseph Lipman
ISBN-10 9783540854203
Release 2009-03-07
Pages 478
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Part One of this book covers the abstract foundations of Grothendieck duality theory for schemes in part with noetherian hypotheses and with some refinements for maps of finite tor-dimension. Part Two extends the theory to the context of diagrams of schemes.

Algebraic Cobordism

Algebraic Cobordism Author Marc Levine
ISBN-10 9783540368243
Release 2007-02-23
Pages 246
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Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. The book also contains some examples of computations and applications.

Rational Representations of Algebraic Groups

Rational Representations of Algebraic Groups Author Stephen Donkin
ISBN-10 9783540395898
Release 2006-11-14
Pages 258
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Rational Representations of Algebraic Groups has been writing in one form or another for most of life. You can find so many inspiration from Rational Representations of Algebraic Groups also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Rational Representations of Algebraic Groups book for free.

Rational Algebraic Curves

Rational Algebraic Curves Author J. Rafael Sendra
ISBN-10 9783540737254
Release 2007-12-10
Pages 270
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The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. The book discusses various optimality criteria for rational parametrizations of algebraic curves.

Topological and Algebraic Structures in Fuzzy Sets

Topological and Algebraic Structures in Fuzzy Sets Author S.E. Rodabaugh
ISBN-10 9789401702317
Release 2013-03-14
Pages 470
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This volume summarizes recent developments in the topological and algebraic structures in fuzzy sets and may be rightly viewed as a continuation of the stan dardization of the mathematics of fuzzy sets established in the "Handbook", namely the Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Volume 3 of The Handbooks of Fuzzy Sets Series (Kluwer Academic Publish ers, 1999). Many of the topological chapters of the present work are not only based upon the foundations and notation for topology laid down in the Hand book, but also upon Handbook developments in convergence, uniform spaces, compactness, separation axioms, and canonical examples; and thus this work is, with respect to topology, a continuation of the standardization of the Hand book. At the same time, this work significantly complements the Handbook in regard to algebraic structures. Thus the present volume is an extension of the content and role of the Handbook as a reference work. On the other hand, this volume, even as the Handbook, is a culmination of mathematical developments motivated by the renowned International Sem inar on Fuzzy Set Theory, also known as the Linz Seminar, held annually in Linz, Austria. Much of the material of this volume is related to the Twenti eth Seminar held in February 1999, material for which the Seminar played a crucial and stimulating role, especially in providing feedback, connections, and the necessary screening of ideas.

Handbook of Combinatorics

Handbook of Combinatorics Author
ISBN-10 9780444880024
Release 1995
Pages 1178
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Handbook of Combinatorics has been writing in one form or another for most of life. You can find so many inspiration from Handbook of Combinatorics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Handbook of Combinatorics book for free.

Advanced Combinatorics

Advanced Combinatorics Author Louis Comtet
ISBN-10 9789401021968
Release 2012-12-06
Pages 343
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Notwithstanding its title, the reader will not find in this book a systematic account of this huge subject. Certain classical aspects have been passed by, and the true title ought to be "Various questions of elementary combina torial analysis". For instance, we only touch upon the subject of graphs and configurations, but there exists a very extensive and good literature on this subject. For this we refer the reader to the bibliography at the end of the volume. The true beginnings of combinatorial analysis (also called combina tory analysis) coincide with the beginnings of probability theory in the 17th century. For about two centuries it vanished as an autonomous sub ject. But the advance of statistics, with an ever-increasing demand for configurations as well as the advent and development of computers, have, beyond doubt, contributed to reinstating this subject after such a long period of negligence. For a long time the aim of combinatorial analysis was to count the different ways of arranging objects under given circumstances. Hence, many of the traditional problems of analysis or geometry which are con cerned at a certain moment with finite structures, have a combinatorial character. Today, combinatorial analysis is also relevant to problems of existence, estimation and structuration, like all other parts of mathema tics, but exclusively forjinite sets.

Noncommutative Motives

Noncommutative Motives Author Gonçalo Tabuada
ISBN-10 9781470423971
Release 2015-09-21
Pages 114
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The theory of motives began in the early 1960s when Grothendieck envisioned the existence of a "universal cohomology theory of algebraic varieties". The theory of noncommutative motives is more recent. It began in the 1980s when the Moscow school (Beilinson, Bondal, Kapranov, Manin, and others) began the study of algebraic varieties via their derived categories of coherent sheaves, and continued in the 2000s when Kontsevich conjectured the existence of a "universal invariant of noncommutative algebraic varieties". This book, prefaced by Yuri I. Manin, gives a rigorous overview of some of the main advances in the theory of noncommutative motives. It is divided into three main parts. The first part, which is of independent interest, is devoted to the study of DG categories from a homotopical viewpoint. The second part, written with an emphasis on examples and applications, covers the theory of noncommutative pure motives, noncommutative standard conjectures, noncommutative motivic Galois groups, and also the relations between these notions and their commutative counterparts. The last part is devoted to the theory of noncommutative mixed motives. The rigorous formalization of this latter theory requires the language of Grothendieck derivators, which, for the reader's convenience, is revised in a brief appendix.

Coulomb Frames in the Normal Bundle of Surfaces in Euclidean Spaces

Coulomb Frames in the Normal Bundle of Surfaces in Euclidean Spaces Author Steffen Fröhlich
ISBN-10 9783642298462
Release 2012-06-30
Pages 117
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This book is intended for advanced students and young researchers interested in the analysis of partial differential equations and differential geometry. It discusses elementary concepts of surface geometry in higher-dimensional Euclidean spaces, in particular the differential equations of Gauss-Weingarten together with various integrability conditions and corresponding surface curvatures. It includes a chapter on curvature estimates for such surfaces, and, using results from potential theory and harmonic analysis, it addresses geometric and analytic methods to establish the existence and regularity of Coulomb frames in their normal bundles, which arise as critical points for a functional of total torsion.

Mathematics of Planet Earth

Mathematics of Planet Earth Author Eulogio Pardo-Igúzquiza
ISBN-10 9783642324086
Release 2013-10-07
Pages 861
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It is widely recognized that the degree of development of a science is given by the transition from a mainly descriptive stage to a more quantitative stage. In this transition, qualitative interpretations (conceptual models) are complemented with quantification (numerical models, both, deterministic and stochastic). This has been the main task of mathematical geoscientists during the last forty years - to establish new frontiers and new challenges in the study and understanding of the natural world. Mathematics of Planet Earth comprises the proceedings of the International Association for Mathematical Geosciences Conference (IAMG2013), held in Madrid from September 2-6, 2013. The Conference addresses researchers, professionals and students. The proceedings contain more than 150 original contributions and give a multidisciplinary vision of mathematical geosciences.

Evolutionary Computation for Modeling and Optimization

Evolutionary Computation for Modeling and Optimization Author Daniel Ashlock
ISBN-10 0387319093
Release 2006-04-04
Pages 572
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Concentrates on developing intuition about evolutionary computation and problem solving skills and tool sets. Lots of applications and test problems, including a biotechnology chapter.

Books in Series

Books in Series Author
ISBN-10 UOM:39015021462695
Release 1985
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Books in Series has been writing in one form or another for most of life. You can find so many inspiration from Books in Series also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Books in Series book for free.