Partial Dynamical Systems Fell Bundles And Applications

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Partial Dynamical Systems, Fell Bundles and Applications

Ruy Exel
Partial Dynamical Systems Fell Bundles and Applications Book PDF

Author : Ruy Exel
Publisher : American Mathematical Soc.
Page : 321 pages
File Size : 50,7 Mb
Release : 2017-09-20
Category : Banach spaces
ISBN : 9781470437855

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Partial Dynamical Systems, Fell Bundles and Applications by Ruy Exel Pdf

Partial dynamical systems, originally developed as a tool to study algebras of operators in Hilbert spaces, has recently become an important branch of algebra. Its most powerful results allow for understanding structural properties of algebras, both in the purely algebraic and in the C*-contexts, in terms of the dynamical properties of certain systems which are often hiding behind algebraic structures. The first indication that the study of an algebra using partial dynamical systems may be helpful is the presence of a grading. While the usual theory of graded algebras often requires gradings to be saturated, the theory of partial dynamical systems is especially well suited to treat nonsaturated graded algebras which are in fact the source of the notion of “partiality”. One of the main results of the book states that every graded algebra satisfying suitable conditions may be reconstructed from a partial dynamical system via a process called the partial crossed product. Running in parallel with partial dynamical systems, partial representations of groups are also presented and studied in depth. In addition to presenting main theoretical results, several specific examples are analyzed, including Wiener–Hopf algebras and graph C*-algebras.

Advances in Mathematics and Applications

Carlile Lavor,Francisco A. M. Gomes
Advances in Mathematics and Applications Book PDF

Author : Carlile Lavor,Francisco A. M. Gomes
Publisher : Springer
Page : 407 pages
File Size : 54,9 Mb
Release : 2018-09-07
Category : Mathematics
ISBN : 9783319940151

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Advances in Mathematics and Applications by Carlile Lavor,Francisco A. M. Gomes Pdf

This book celebrates the 50th anniversary of the Institute of Mathematics, Statistics and Scientific Computing (IMECC) of the University of Campinas, Brazil, by offering reviews of selected research developed at one of the most prestigious mathematics institutes in Latin America. Written by senior professors at the IMECC, it covers topics in pure and applied mathematics and statistics ranging from differential geometry, dynamical systems, Lie groups, and partial differential equations to computational optimization, mathematical physics, stochastic process, time series, and more. A report on the challenges and opportunities of research in applied mathematics - a highly active field of research in the country - and highlights of the Institute since its foundation in 1968 completes this historical volume, which is unveiled in the same year that the International Mathematical Union (IMU) names Brazil as a member of the Group V of countries with the most relevant contributions in mathematics.

Operator Algebras and Applications

Toke M. Carlsen,Nadia S. Larsen,Sergey Neshveyev,Christian Skau
Operator Algebras and Applications Book PDF

Author : Toke M. Carlsen,Nadia S. Larsen,Sergey Neshveyev,Christian Skau
Publisher : Springer
Page : 348 pages
File Size : 49,7 Mb
Release : 2016-07-30
Category : Mathematics
ISBN : 9783319392868

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Operator Algebras and Applications by Toke M. Carlsen,Nadia S. Larsen,Sergey Neshveyev,Christian Skau Pdf

Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras. It is interesting to see the remarkable advances that have been made in operator algebras over these years, which strikingly illustrate the vitality of the field. A total of 26 talks were given at the symposium on a variety of themes, all highlighting the richness of the subject. The field of operator algebras was created in the 1930s and was motivated by problems of quantum mechanics. It has subsequently developed well beyond its initial intended realm of applications and expanded into such diverse areas of mathematics as representation theory, dynamical systems, differential geometry, number theory and quantum algebra. One branch, known as “noncommutative geometry”, has become a powerful tool for studying phenomena that are beyond the reach of classical analysis. This volume includes research papers that present new results, surveys that discuss the development of a specific line of research, and articles that offer a combination of survey and research. These contributions provide a multifaceted portrait of beautiful mathematics that both newcomers to the field of operator algebras and seasoned researchers alike will appreciate.

Linear and Quasilinear Parabolic Systems: Sobolev Space Theory

David Hoff
Linear and Quasilinear Parabolic Systems Sobolev Space Theory Book PDF

Author : David Hoff
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 41,5 Mb
Release : 2020-11-18
Category : Education
ISBN : 9781470461614

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Linear and Quasilinear Parabolic Systems: Sobolev Space Theory by David Hoff Pdf

This monograph presents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients. Applications to quasilinear systems are given, including local existence for large data, global existence near an attractor, the Leray and Hopf theorems for the Navier-Stokes equations and results concerning invariant regions. Supplementary material is provided, including a self-contained treatment of the calculus of Sobolev functions on the boundaries of Lipschitz domains and a thorough discussion of measurability considerations for elements of Bochner-Sobolev spaces. This book will be particularly useful both for researchers requiring accessible and broadly applicable formulations of standard results as well as for students preparing for research in applied analysis. Readers should be familiar with the basic facts of measure theory and functional analysis, including weak derivatives and Sobolev spaces. Prior work in partial differential equations is helpful but not required.

K-Theory for Group C*-Algebras and Semigroup C*-Algebras

Joachim Cuntz,Siegfried Echterhoff,Xin Li,Guoliang Yu
K Theory for Group C Algebras and Semigroup C Algebras Book PDF

Author : Joachim Cuntz,Siegfried Echterhoff,Xin Li,Guoliang Yu
Publisher : Birkhäuser
Page : 322 pages
File Size : 40,7 Mb
Release : 2017-10-24
Category : Mathematics
ISBN : 9783319599151

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K-Theory for Group C*-Algebras and Semigroup C*-Algebras by Joachim Cuntz,Siegfried Echterhoff,Xin Li,Guoliang Yu Pdf

This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions. Part of the most basic structural information for such a C*-algebra is contained in its K-theory. The determination of the K-groups of C*-algebras constructed from group or semigroup actions is a particularly challenging problem. Paul Baum and Alain Connes proposed a formula for the K-theory of the reduced crossed product for a group action that would permit, in principle, its computation. By work of many hands, the formula has by now been verified for very large classes of groups and this work has led to the development of a host of new techniques. An important ingredient is Kasparov's bivariant K-theory. More recently, also the C*-algebras generated by the regular representation of a semigroup as well as the crossed products for actions of semigroups by endomorphisms have been studied in more detail. Intriguing examples of actions of such semigroups come from ergodic theory as well as from algebraic number theory. The computation of the K-theory of the corresponding crossed products needs new techniques. In cases of interest the K-theory of the algebras reflects ergodic theoretic or number theoretic properties of the action.

Jordan Triple Systems in Complex and Functional Analysis

José M. Isidro
Jordan Triple Systems in Complex and Functional Analysis Book PDF

Author : José M. Isidro
Publisher : American Mathematical Soc.
Page : 560 pages
File Size : 45,9 Mb
Release : 2019-12-09
Category : Education
ISBN : 9781470450830

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Jordan Triple Systems in Complex and Functional Analysis by José M. Isidro Pdf

This book is a systematic account of the impressive developments in the theory of symmetric manifolds achieved over the past 50 years. It contains detailed and friendly, but rigorous, proofs of the key results in the theory. Milestones are the study of the group of holomomorphic automorphisms of bounded domains in a complex Banach space (Vigué and Upmeier in the late 1970s), Kaup's theorem on the equivalence of the categories of symmetric Banach manifolds and that of hermitian Jordan triple systems, and the culminating point in the process: the Riemann mapping theorem for complex Banach spaces (Kaup, 1982). This led to the introduction of wide classes of Banach spaces known as JB∗-triples and JBW∗-triples whose geometry has been thoroughly studied by several outstanding mathematicians in the late 1980s. The book presents a good example of fruitful interaction between different branches of mathematics, making it attractive for mathematicians interested in various fields such as algebra, differential geometry and, of course, complex and functional analysis.

Weak Convergence of Measures

Vladimir I. Bogachev
Weak Convergence of Measures Book PDF

Author : Vladimir I. Bogachev
Publisher : American Mathematical Soc.
Page : 286 pages
File Size : 47,9 Mb
Release : 2018-09-27
Category : Convergence
ISBN : 9781470447380

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Weak Convergence of Measures by Vladimir I. Bogachev Pdf

This book provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and other theoretical and applied fields. Particular attention is given to weak convergence of measures. The principal material is oriented toward a broad circle of readers dealing with convergence in distribution of random variables and weak convergence of measures. The book contains the necessary background from measure theory and functional analysis. Large complementary sections aimed at researchers present the most important recent achievements. More than 100 exercises (ranging from easy introductory exercises to rather difficult problems for experienced readers) are given with hints, solutions, or references. Historic and bibliographic comments are included. The target readership includes mathematicians and physicists whose research is related to probability theory, mathematical statistics, functional analysis, and mathematical physics.

The Classification of the Finite Simple Groups, Number 8: Part III, Chapters 12–17: The Generic Case, Completed

Daniel Gorenstein,Richard Lyons,Ronald Solomon
The Classification of the Finite Simple Groups Number 8 Part III Chapters 12 17 The Generic Case Completed Book PDF

Author : Daniel Gorenstein,Richard Lyons,Ronald Solomon
Publisher : American Mathematical Soc.
Page : 488 pages
File Size : 42,6 Mb
Release : 2018-12-12
Category : Electronic
ISBN : 9781470441890

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The Classification of the Finite Simple Groups, Number 8: Part III, Chapters 12–17: The Generic Case, Completed by Daniel Gorenstein,Richard Lyons,Ronald Solomon Pdf

This book completes a trilogy (Numbers 5, 7, and 8) of the series The Classification of the Finite Simple Groups treating the generic case of the classification of the finite simple groups. In conjunction with Numbers 4 and 6, it allows us to reach a major milestone in our series—the completion of the proof of the following theorem: Theorem O: Let G be a finite simple group of odd type, all of whose proper simple sections are known simple groups. Then either G is an alternating group or G is a finite group of Lie type defined over a field of odd order or G is one of six sporadic simple groups. Put another way, Theorem O asserts that any minimal counterexample to the classification of the finite simple groups must be of even type. The work of Aschbacher and Smith shows that a minimal counterexample is not of quasithin even type, while this volume shows that a minimal counterexample cannot be of generic even type, modulo the treatment of certain intermediate configurations of even type which will be ruled out in the next volume of our series.

The Adams Spectral Sequence for Topological Modular Forms

Robert R. Bruner,John Rognes
The Adams Spectral Sequence for Topological Modular Forms Book PDF

Author : Robert R. Bruner,John Rognes
Publisher : American Mathematical Society
Page : 690 pages
File Size : 47,5 Mb
Release : 2021-12-23
Category : Mathematics
ISBN : 9781470469580

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The Adams Spectral Sequence for Topological Modular Forms by Robert R. Bruner,John Rognes Pdf

The connective topological modular forms spectrum, $tmf$, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy of $tmf$ and several $tmf$-module spectra by means of the classical Adams spectral sequence, thus verifying, correcting, and extending existing approaches. In the process, folklore results are made precise and generalized. Anderson and Brown-Comenetz duality, and the corresponding dualities in homotopy groups, are carefully proved. The volume also includes an account of the homotopy groups of spheres through degree 44, with complete proofs, except that the Adams conjecture is used without proof. Also presented are modern stable proofs of classical results which are hard to extract from the literature. Tools used in this book include a multiplicative spectral sequence generalizing a construction of Davis and Mahowald, and computer software which computes the cohomology of modules over the Steenrod algebra and products therein. Techniques from commutative algebra are used to make the calculation precise and finite. The $H$-infinity ring structure of the sphere and of $tmf$ are used to determine many differentials and relations.

The Classification of the Finite Simple Groups, Number 9

Inna Capdeboscq,Daniel Gorenstein,Richard Lyons,Ronald Solomon
The Classification of the Finite Simple Groups Number 9 Book PDF

Author : Inna Capdeboscq,Daniel Gorenstein,Richard Lyons,Ronald Solomon
Publisher : American Mathematical Society
Page : 520 pages
File Size : 46,9 Mb
Release : 2021-02-22
Category : Mathematics
ISBN : 9781470464370

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The Classification of the Finite Simple Groups, Number 9 by Inna Capdeboscq,Daniel Gorenstein,Richard Lyons,Ronald Solomon Pdf

This book is the ninth volume in a series whose goal is to furnish a careful and largely self-contained proof of the classification theorem for the finite simple groups. Having completed the classification of the simple groups of odd type as well as the classification of the simple groups of generic even type (modulo uniqueness theorems to appear later), the current volume begins the classification of the finite simple groups of special even type. The principal result of this volume is a classification of the groups of bicharacteristic type, i.e., of both even type and of $p$-type for a suitable odd prime $p$. It is here that the largest sporadic groups emerge, namely the Monster, the Baby Monster, the largest Conway group, and the three Fischer groups, along with six finite groups of Lie type over small fields, several of which play a major role as subgroups or sections of these sporadic groups.

Local Operators in Integrable Models I

Michio Jimbo,Tetsuji Miwa,Fedor Smirnov
Local Operators in Integrable Models I Book PDF

Author : Michio Jimbo,Tetsuji Miwa,Fedor Smirnov
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 52,9 Mb
Release : 2021-07-02
Category : Education
ISBN : 9781470465520

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Local Operators in Integrable Models I by Michio Jimbo,Tetsuji Miwa,Fedor Smirnov Pdf

Integrable models in statistical mechanics and quantum field theory constitute a rich research field at the crossroads of modern mathematics and theoretical physics. An important issue to understand is the space of local operators in the system and, ultimately, their correlation functions and form factors. This book is the first published monograph on this subject. It treats integrable lattice models, notably the six-vertex model and the XXZ Heisenberg spin chain. A pair of fermions is introduced and used to create a basis of the space of local operators, leading to the result that all correlation functions at finite distances are expressible in terms of two transcendental functions with rational coefficients. Step-by-step explanations are given for all materials necessary for this construction, ranging from algebraic Bethe ansatz, representations of quantum groups, and the Bazhanov-Lukyanov-Zamolodchikov construction in conformal field theory to Riemann surfaces and their Jacobians. Several examples and applications are given along with numerical results. Going through the book, readers will find themselves at the forefront of this rapidly developing research field.

Numerical Algorithms for Number Theory: Using Pari/GP

Karim Belabas,Henri Cohen
Numerical Algorithms for Number Theory Using Pari GP Book PDF

Author : Karim Belabas,Henri Cohen
Publisher : American Mathematical Soc.
Page : 429 pages
File Size : 52,7 Mb
Release : 2021-06-23
Category : Education
ISBN : 9781470463519

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Numerical Algorithms for Number Theory: Using Pari/GP by Karim Belabas,Henri Cohen Pdf

This book presents multiprecision algorithms used in number theory and elsewhere, such as extrapolation, numerical integration, numerical summation (including multiple zeta values and the Riemann-Siegel formula), evaluation and speed of convergence of continued fractions, Euler products and Euler sums, inverse Mellin transforms, and complex L L-functions. For each task, many algorithms are presented, such as Gaussian and doubly-exponential integration, Euler-MacLaurin, Abel-Plana, Lagrange, and Monien summation. Each algorithm is given in detail, together with a complete implementation in the free Pari/GP system. These implementations serve both to make even more precise the inner workings of the algorithms, and to gently introduce advanced features of the Pari/GP language. This book will be appreciated by anyone interested in number theory, specifically in practical implementations, computer experiments and numerical algorithms that can be scaled to produce thousands of digits of accuracy.

One-Dimensional Turbulence and the Stochastic Burgers Equation

Alexandre Boritchev,Sergei Kuksin
One Dimensional Turbulence and the Stochastic Burgers Equation Book PDF

Author : Alexandre Boritchev,Sergei Kuksin
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 44,6 Mb
Release : 2021-07-01
Category : Education
ISBN : 9781470464363

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One-Dimensional Turbulence and the Stochastic Burgers Equation by Alexandre Boritchev,Sergei Kuksin Pdf

This book is dedicated to the qualitative theory of the stochastic one-dimensional Burgers equation with small viscosity under periodic boundary conditions and to interpreting the obtained results in terms of one-dimensional turbulence in a fictitious one-dimensional fluid described by the Burgers equation. The properties of one-dimensional turbulence which we rigorously derive are then compared with the heuristic Kolmogorov theory of hydrodynamical turbulence, known as the K41 theory. It is shown, in particular, that these properties imply natural one-dimensional analogues of three principal laws of the K41 theory: the size of the Kolmogorov inner scale, the 2/3 2/3-law, and the Kolmogorov–Obukhov law. The first part of the book deals with the stochastic Burgers equation, including the inviscid limit for the equation, its asymptotic in time behavior, and a theory of generalised L 1 L1-solutions. This section makes a self-consistent introduction to stochastic PDEs. The relative simplicity of the model allows us to present in a light form many of the main ideas from the general theory of this field. The second part, dedicated to the relation of one-dimensional turbulence with the K41 theory, could serve for a mathematical reader as a rigorous introduction to the literature on hydrodynamical turbulence, all of which is written on a physical level of rigor.

The Cremona Group and Its Subgroups

Julie Déserti
The Cremona Group and Its Subgroups Book PDF

Author : Julie Déserti
Publisher : American Mathematical Soc.
Page : 187 pages
File Size : 50,8 Mb
Release : 2021-04-13
Category : Education
ISBN : 9781470460129

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The Cremona Group and Its Subgroups by Julie Déserti Pdf

The goal of this book is to present a portrait of the n n-dimensional Cremona group with an emphasis on the 2-dimensional case. After recalling some crucial tools, the book describes a naturally defined infinite dimensional hyperbolic space on which the Cremona group acts. This space plays a fundamental role in the study of Cremona groups, as it allows one to apply tools from geometric group theory to explore properties of the subgroups of the Cremona group as well as the degree growth and dynamical behavior of birational transformations. The book describes natural topologies on the Cremona group, codifies the notion of algebraic subgroups of the Cremona groups and finishes with a chapter on the dynamics of their actions. This book is aimed at graduate students and researchers in algebraic geometry who are interested in birational geometry and its interactions with geometric group theory and dynamical systems.

K-theory in Algebra, Analysis and Topology

Guillermo Cortiñas,Charles A. Weibel
K theory in Algebra Analysis and Topology Book PDF

Author : Guillermo Cortiñas,Charles A. Weibel
Publisher : American Mathematical Soc.
Page : 388 pages
File Size : 45,5 Mb
Release : 2024-06-02
Category : Education
ISBN : 9781470450267

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K-theory in Algebra, Analysis and Topology by Guillermo Cortiñas,Charles A. Weibel Pdf

This volume contains the proceedings of the ICM 2018 satellite school and workshop K-theory conference in Argentina. The school was held from July 16–20, 2018, in La Plata, Argentina, and the workshop was held from July 23–27, 2018, in Buenos Aires, Argentina. The volume showcases current developments in K-theory and related areas, including motives, homological algebra, index theory, operator algebras, and their applications and connections. Papers cover topics such as K-theory of group rings, Witt groups of real algebraic varieties, coarse homology theories, topological cyclic homology, negative K-groups of monoid algebras, Milnor K-theory and regulators, noncommutative motives, the classification of C∗-algebras via Kasparov's K-theory, the comparison between full and reduced C∗-crossed products, and a proof of Bott periodicity using almost commuting matrices.