Several Topics In Singularity Theory
DOWNLOAD
Download Several Topics In Singularity Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Several Topics In Singularity Theory book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Topics On Real And Complex Singularities
DOWNLOAD
Author : Satoshi Koike
language : en
Publisher: World Scientific
Release Date : 2014-04-02
Topics On Real And Complex Singularities written by Satoshi Koike and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-02 with Mathematics categories.
A phenomenon which appears in nature, or human behavior, can sometimes be explained by saying that a certain potential function is maximized, or minimized. For example, the Hamiltonian mechanics, soapy films, size of an atom, business management, etc. In mathematics, a point where a given function attains an extreme value is called a critical point, or a singular point. The purpose of singularity theory is to explore the properties of singular points of functions and mappings.This is a volume on the proceedings of the fourth Japanese-Australian Workshop on Real and Complex Singularities held in Kobe, Japan. It consists of 11 original articles on singularities. Readers will be introduced to some important new notions for characterizations of singularities and several interesting results are delivered. In addition, current approaches to classical topics and state-of-the-art effective computational methods of invariants of singularities are also presented. This volume will be useful not only to the singularity theory specialists but also to general mathematicians.
Singularity Theory And Gravitational Lensing
DOWNLOAD
Author : Arlie O. Petters
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singularity Theory And Gravitational Lensing written by Arlie O. Petters and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Astronomers do not do experiments. They observe the universe primarily through detect ing light emitted by stars and other luminous objects. Since this light must travel through space to reach us, variations in the metric of space affects the appearance of astronomical objects. These variations lead to dramatic changes in the shape and brightness of astronom ical sources. Because these variations are sensitive to mass rather than to light, observations of gravitational lensing enable astronomers to probe the mass distribution of the universe. With gravitational lensing observations, astronomers are addressing many of the most important scientific questions in astronomy and physics: • What is the universe made of? Most of the energy and mass in the universe is not in the form of luminous objects. Stars account for less than 1 % of the energy density of the universe. Perhaps, as much as another 3% of the energy density of the universe is in the form of warm gas that fills the space between galaxies. The remaining 96% of the energy density is in some yet unidentified form. Roughly one third of this energy density of the universe is "dark matter," matter that clusters gravitationally but does not emit light. Most cosmologists suspect that this dark matter is composed of weakly interacting subatomic particles. However, most of the energy density of the universe appears to be in an even stranger form: energy associated with empty space.
Real And Complex Singularities
DOWNLOAD
Author : Laurentiu Paunescu
language : en
Publisher: World Scientific
Release Date : 2007
Real And Complex Singularities written by Laurentiu Paunescu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The modern theory of singularities provides a unifying theme that runs through fields of mathematics as diverse as homological algebra and Hamiltonian systems. It is also an important point of reference in the development of a large part of contemporary algebra, geometry and analysis. Presented by internationally recognized experts, the collection of articles in this volume yields a significant cross-section of these developments. The wide range of surveys includes an authoritative treatment of the deformation theory of isolated complex singularities by prize-winning researcher K Miyajima. Graduate students and even ambitious undergraduates in mathematics will find many research ideas in this volume and non-experts in mathematics can have an overview of some classic and fundamental results in singularity theory. The explanations are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.
Handbook Of Geometry And Topology Of Singularities Vii
DOWNLOAD
Author : José Luis Cisneros-Molina
language : en
Publisher: Springer Nature
Release Date : 2025-03-01
Handbook Of Geometry And Topology Of Singularities Vii written by José Luis Cisneros-Molina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-01 with Mathematics categories.
This is the seventh volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of fourteen chapters that provide an in-depth and reader-friendly introduction to various important aspects of singularity theory. The volume begins with an outstanding exposition on Jim Damon’s contributions to singularity theory and its applications. Jim passed away in 2022 and he was one of the greatest mathematicians of recent times, having made remarkable contributions to singularity theory and its applications, mostly to medical image computing. The next chapter focuses on the singularities of real functions and their bifurcation sets. Then, we look at the perturbation theory of polynomials and linear operators, complex analytic frontal singularities, the global singularity theory of differentiable maps, and the singularities of holomorphic functions from a global point of view. The volume continues with an overview of new tools in singularity theory that spring from symplectic geometry and Floer-type homology theories. Then, it looks at the derivation of Lie algebras of isolated singularities and the three-dimensional rational isolated complete intersection singularities, as well as recent developments in algebraic K-stability and the stable degeneration conjecture. This volume also contains an interesting survey on V-filtrations, a theory began by Malgrange and Kashiwara that can be used to study nearby and vanishing cycle functors and introduced by Deligne. Then, we present a panoramic view of the Hodge, toric, and motivic methods in the study of Milnor fibers in singularity theory, both from local and global points of view. The Monodromy conjecture is also explained; this is a longstanding open problem in singularity theory that lies at the crossroads of number theory, algebra, analysis, geometry, and topology. This volume closes with recent developments in the study of the algebraic complexity of optimization problems in applied algebraic geometry and algebraic statistics. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Several Topics In Singularity Theory
DOWNLOAD
Author : Satoshi Koike
language : en
Publisher:
Release Date : 2003
Several Topics In Singularity Theory written by Satoshi Koike and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
Singularities And Groups In Bifurcation Theory
DOWNLOAD
Author : Martin Golubitsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Singularities And Groups In Bifurcation Theory written by Martin Golubitsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob lems and we hope to convert the reader to this view. In this preface we will discuss what we feel are the strengths of the singularity theory approach. This discussion then Ieads naturally into a discussion of the contents of the book and the prerequisites for reading it. Let us emphasize that our principal contribution in this area has been to apply pre-existing techniques from singularity theory, especially unfolding theory and classification theory, to bifurcation problems. Many ofthe ideas in this part of singularity theory were originally proposed by Rene Thom; the subject was then developed rigorously by John Matherand extended by V. I. Arnold. In applying this material to bifurcation problems, we were greatly encouraged by how weil the mathematical ideas of singularity theory meshed with the questions addressed by bifurcation theory. Concerning our title, Singularities and Groups in Bifurcation Theory, it should be mentioned that the present text is the first volume in a two-volume sequence. In this volume our emphasis is on singularity theory, with group theory playing a subordinate role. In Volume II the emphasis will be more balanced. Having made these remarks, Iet us set the context for the discussion of the strengths of the singularity theory approach to bifurcation. As we use the term, bifurcation theory is the study of equations with multiple solutions.
Handbook Of Geometry And Topology Of Singularities Iv
DOWNLOAD
Author : José Luis Cisneros-Molina
language : en
Publisher: Springer Nature
Release Date : 2023-10-07
Handbook Of Geometry And Topology Of Singularities Iv written by José Luis Cisneros-Molina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-07 with Mathematics categories.
This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex. Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Handbook Of Geometry And Topology Of Singularities V Foliations
DOWNLOAD
Author : Felipe Cano
language : en
Publisher: Springer Nature
Release Date : 2024-06-05
Handbook Of Geometry And Topology Of Singularities V Foliations written by Felipe Cano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-05 with Mathematics categories.
This is the fifth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. Singularities are ubiquitous in mathematics and science in general, and singularity theory is a crucible where different types of mathematical problems converge, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. This Volume V focuses on singular holomorphic foliations, which is a multidisciplinary field and a whole area of mathematics in itself. Singular foliations arise, for instance, by considering: The fibers of a smooth map between differentiable manifolds, with singularities at the critical points. The integral lines of a vector field, or the action of a Lie group on a manifold. The singularities are the orbits with special isotropy. The kernel of appropriate 1-forms. The singularities are the zeros of the form. Open books, which naturally appear in singularity theory as foliations with singular set the binding. These important examples highlight the deep connections between foliations and singularity theory. This volume, like its companion Volume VI, also focused on foliations, consists of nine chapters, authored by world experts, which provide in-depth and reader-friendly introductions to some of the foundational aspects of the theory. These introductions also give insights into important lines of further research. The volume starts with a foreword by one of the current world leaders in the theory of complex foliations. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Normal Surface Singularities
DOWNLOAD
Author : András Némethi
language : en
Publisher: Springer Nature
Release Date : 2022-10-07
Normal Surface Singularities written by András Némethi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-07 with Mathematics categories.
This monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology. In this way, it unites the analytic approach with the more recent topological one, combining their tools and methods. In the first chapters, the book sets out the foundations of the theory of normal surface singularities. This includes a comprehensive presentation of the properties of the link (as an oriented 3-manifold) and of the invariants associated with a resolution, combined with the structure and special properties of the line bundles defined on a resolution. A recurring theme is the comparison of analytic and topological invariants. For example, the Poincaré series of the divisorial filtration is compared to a topological zeta function associated with the resolution graph, and the sheaf cohomologies of the line bundles are compared to the Seiberg–Witten invariants of the link. Equivariant Ehrhart theory is introduced to establish surgery-additivity formulae of these invariants, as well as for the regularization procedures of multivariable series. In addition to recent research, the book also provides expositions of more classical subjects such as the classification of plane and cuspidal curves, Milnor fibrations and smoothing invariants, the local divisor class group, and the Hilbert–Samuel function. It contains a large number of examples of key families of germs: rational, elliptic, weighted homogeneous, superisolated and splice-quotient. It provides concrete computations of the topological invariants of their links (Casson(–Walker) and Seiberg–Witten invariants, Turaev torsion) and of the analytic invariants (geometric genus, Hilbert function of the divisorial filtration, and the analytic semigroup associated with the resolution). The book culminates in a discussion of the topological and analytic lattice cohomologies (as categorifications of the Seiberg–Witten invariant and of the geometric genus respectively) and of the graded roots. Several open problems and conjectures are also formulated. Normal Surface Singularities provides researchers in algebraic and differential geometry, singularity theory, complex analysis, and low-dimensional topology with an invaluable reference on this rich topic, offering a unified presentation of the major results and approaches.
Singularity Theory
DOWNLOAD
Author : Bill Bruce
language : en
Publisher: Cambridge University Press
Release Date : 1999-06-03
Singularity Theory written by Bill Bruce and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-03 with Computers categories.
An up-to-date survey of research in singularity theory.