Formal Moduli of Algebraic Structures
Author: O. A. Laudal
Publisher: Springer
Published: 2006-11-15
Total Pages: 165
ISBN-13: 3540385320
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Advances in Queueing Theory and Network Applications
Author: Wuyi Yue
Publisher: Springer
Published: 2008-12-19
Total Pages: 316
ISBN-13: 9780387097022
DOWNLOAD EBOOKAdvances in Queueing Theory and Network Applications presents several useful mathematical analyses in queueing theory and mathematical models of key technologies in wired and wireless communication networks such as channel access controls, Internet applications, topology construction, energy saving schemes, and transmission scheduling. In sixteen high quality chapters, this work provides novel ideas, new analytical models, and simulation and experimental results by experts in the field of queueing theory and network applications. The text serves as a state-of-the-art reference for a wide range of researchers and engineers engaged in the fields of queueing theory and network applications, and can also serve as supplemental material for advanced courses in operations research, queueing theory, performance analysis, traffic theory, as well as theoretical design and management of communication networks.
Algebraic Structures and Moduli Spaces
Author: Jacques Hurtubise
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 266
ISBN-13: 0821835688
DOWNLOAD EBOOKThis book contains recent and exciting developments on the structure of moduli spaces, with an emphasis on the algebraic structures that underlie this structure. Topics covered include Hilbert schemes of points, moduli of instantons, coherent sheaves and their derived categories, moduli of flat connections, Hodge structures, and the topology of affine varieties. Two beautiful series of lectures are a particularly fine feature of the book. One is an introductory series by Manfred Lehn on the topology and geometry of Hilbert schemes of points on surfaces, and the other, by Hiraku Nakajima and Kota Yoshioka, explains their recent work on the moduli space of instantons over ${\mathbb R 4$. The material is suitable for graduate students and researchers interested in moduli spaces in algebraic geometry, topology, and mathematical physics.
Algebraic Structures
Author: George R. Kempf
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 174
ISBN-13: 3322802787
DOWNLOAD EBOOKIn algebra there are four basic structures: groups, rings, fields and modules. In this book the theory of these basic structures is presented and the laws of composition - the basic operations of algebra - are studied. Essentially, no previous knowledge is required, it is only assumed as background that the reader has learned some linear algebra over the real numbers.Dieses Lehrbuch, verfasst von einem anerkannten amerikanischen Mathematiker, ist eine unkonventionelle Einführung in die Algebra. Es gibt vier grundlegende Strukturen in der Algebra: Gruppen, Ringe, Körper und Moduln. Das Buch behandelt die Theorie dieser Strukturen und beschreibt die Verknüpfungsregeln, die grundlegenden Operationen der Algebra. Die Darstellung ist elementar: es werden nur Kenntnisse der Linearen Algebra vorausgesetzt, weitere Fachkenntnisse sind nicht erforderlich.
Chern-Simons Theory and Equivariant Factorization Algebras
Author: Corina Keller
Publisher: Springer
Published: 2019-01-25
Total Pages: 154
ISBN-13: 365825338X
DOWNLOAD EBOOKCorina Keller studies non-perturbative facets of abelian Chern-Simons theories. This is a refinement of the entirely perturbative approach to classical Chern-Simons theory via homotopy factorization algebras of observables that arise from the associated formal moduli problem describing deformations of flat principal bundles with connections over the spacetime manifold. The author shows that for theories with abelian group structure, this factorization algebra of classical observables comes naturally equipped with an action of the gauge group, which allows to encode non-perturbative effects in the classical observables. About the Author: Corina Keller currently is a doctoral student in the research group of Prof. Dr. Damien Calaque at the Université Montpellier, France. She is mostly interested in the mathematical study of field theories. Her master’s thesis was supervised by PD Dr. Alessandro Valentino and Prof. Dr. Alberto Cattaneo at Zurich University, Switzerland.
Deformation Spaces
Author: Hossein Abbaspour
Publisher: Springer Science & Business Media
Published: 2010-04-21
Total Pages: 174
ISBN-13: 3834896802
DOWNLOAD EBOOKThe first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since then, deformation theory has been applied as a useful tool in the study of many other mathematical structures, and even today it plays an important role in many developments of modern mathematics. This volume collects a few self-contained and peer-reviewed papers by experts which present up-to-date research topics in algebraic and motivic topology, quantum field theory, algebraic geometry, noncommutative geometry and the deformation theory of Poisson algebras. They originate from activities at the Max-Planck-Institute for Mathematics and the Hausdorff Center for Mathematics in Bonn.
Fundamental Structures of Algebra and Discrete Mathematics
Author: Stephan Foldes
Publisher: John Wiley & Sons
Published: 2011-02-14
Total Pages: 362
ISBN-13: 1118031431
DOWNLOAD EBOOKIntroduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are proved rigorously within the theory of each structure. Throughout the text the reader is frequently prompted to perform integrated exercises of verification and to explore examples.
Associative Algebraic Geometry
Author: Arvid Siqveland
Publisher: World Scientific
Published: 2023-02-17
Total Pages: 420
ISBN-13: 1800613563
DOWNLOAD EBOOKClassical Deformation Theory is used for determining the completions of local rings of an eventual moduli space. When a moduli variety exists, the main result explored in the book is that the local ring in a closed point can be explicitly computed as an algebraization of the pro-representing hull, called the local formal moduli, of the deformation functor for the corresponding closed point.The book gives explicit computational methods and includes the most necessary prerequisites for understanding associative algebraic geometry. It focuses on the meaning and the place of deformation theory, resulting in a complete theory applicable to moduli theory. It answers the question 'why moduli theory', and gives examples in mathematical physics by looking at the universe as a moduli of molecules, thereby giving a meaning to most noncommutative theories.The book contains the first explicit definition of a noncommutative scheme, not necessarily covered by commutative rings. This definition does not contradict any previous abstract definitions of noncommutative algebraic geometry, but sheds interesting light on other theories, which is left for further investigation.
A Study in Derived Algebraic Geometry
Author: Dennis Gaitsgory
Publisher: American Mathematical Soc.
Published: 2017-08-29
Total Pages: 474
ISBN-13: 1470435705
DOWNLOAD EBOOKDerived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in other parts of mathematics, most prominently in representation theory. This volume develops deformation theory, Lie theory and the theory of algebroids in the context of derived algebraic geometry. To that end, it introduces the notion of inf-scheme, which is an infinitesimal deformation of a scheme and studies ind-coherent sheaves on such. As an application of the general theory, the six-functor formalism for D-modules in derived geometry is obtained. This volume consists of two parts. The first part introduces the notion of ind-scheme and extends the theory of ind-coherent sheaves to inf-schemes, obtaining the theory of D-modules as an application. The second part establishes the equivalence between formal Lie group(oids) and Lie algebr(oids) in the category of ind-coherent sheaves. This equivalence gives a vast generalization of the equivalence between Lie algebras and formal moduli problems. This theory is applied to study natural filtrations in formal derived geometry generalizing the Hodge filtration.
An Introduction to Algebraic Structures
Author: Joseph Landin
Publisher: Courier Corporation
Published: 2012-08-29
Total Pages: 275
ISBN-13: 0486150410
DOWNLOAD EBOOKThis self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.
