New Developments In Singularity Theory

Author : Dirk Wiersma,C.T.C. Wall,V. Zakalyukin
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401008341

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New Developments in Singularity Theory by Dirk Wiersma,C.T.C. Wall,V. Zakalyukin Pdf

Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions. The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters. The articles collected here can be grouped under three headings. (A) Singularities of real maps; (B) Singular complex variables; and (C) Singularities of homomorphic maps.

Author : Ray Kurzweil
Publisher : Penguin
Page : 672 pages
File Size : 42,9 Mb
Release : 2005-09-22
Category : Social Science
ISBN : 9781101218884

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The Singularity Is Near by Ray Kurzweil Pdf

“Startling in scope and bravado.” —Janet Maslin, The New York Times “Artfully envisions a breathtakingly better world.” —Los Angeles Times “Elaborate, smart and persuasive.” —The Boston Globe “A pleasure to read.” —The Wall Street Journal One of CBS News’s Best Fall Books of 2005 • Among St Louis Post-Dispatch’s Best Nonfiction Books of 2005 • One of Amazon.com’s Best Science Books of 2005 A radical and optimistic view of the future course of human development from the bestselling author of How to Create a Mind and The Singularity is Nearer who Bill Gates calls “the best person I know at predicting the future of artificial intelligence” For over three decades, Ray Kurzweil has been one of the most respected and provocative advocates of the role of technology in our future. In his classic The Age of Spiritual Machines, he argued that computers would soon rival the full range of human intelligence at its best. Now he examines the next step in this inexorable evolutionary process: the union of human and machine, in which the knowledge and skills embedded in our brains will be combined with the vastly greater capacity, speed, and knowledge-sharing ability of our creations.

Author : Denis Cheniot,Jean-Paul Brasselet
Publisher : World Scientific
Page : 1083 pages
File Size : 45,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812707499

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Singularity Theory by Denis Cheniot,Jean-Paul Brasselet Pdf

The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory. The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.

Author : Shyuichi E. T. Al IZUMIYA
Publisher : World Scientific
Page : 383 pages
File Size : 51,8 Mb
Release : 2015-10-29
Category : Mathematics
ISBN : 9789814590457

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Differential Geometry from a Singularity Theory Viewpoint by Shyuichi E. T. Al IZUMIYA Pdf

"Differential Geometry from a Singularity Theory Viewpoint provides a new look at the fascinating and classical subject of the differential geometry of surfaces in Euclidean spaces. The book uses singularity theory to capture some key geometric features of surfaces. It describes the theory of contact and its link with the theory of caustics and wavefronts. It then uses the powerful techniques of these theories to deduce geometric information about surfaces embedded in 3, 4 and 5-dimensional Euclidean spaces. The book also includes recent work of the authors and their collaborators on the geometry of sub-manifolds in Minkowski spaces."--

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 46,9 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789814477048

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Singularities in Geometry and Topology by Anonim Pdf

Author : James Montaldi
Publisher : Cambridge University Press
Page : 449 pages
File Size : 41,6 Mb
Release : 2021-06-24
Category : Mathematics
ISBN : 9781107151642

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Singularities, Bifurcations and Catastrophes by James Montaldi Pdf

This textbook gives a contemporary account of singularity theory and its principal application, bifurcation theory.

Author : Shihoko Ishii
Publisher : Springer
Page : 227 pages
File Size : 55,9 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9784431550815

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Introduction to Singularities by Shihoko Ishii Pdf

This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundaries of which correspond to singular varieties. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dim ensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied.

Author : Javier Fernández de Bobadilla,Tamás László,András Stipsicz
Publisher : Springer Nature
Page : 332 pages
File Size : 40,7 Mb
Release : 2021-05-27
Category : Mathematics
ISBN : 9783030619589

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Singularities and Their Interaction with Geometry and Low Dimensional Topology by Javier Fernández de Bobadilla,Tamás László,András Stipsicz Pdf

The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory. The papers, written by leading researchers working on various topics of the above fields, are the outcome of the “Némethi60: Geometry and Topology of Singularities” conference held at the Alfréd Rényi Institute of Mathematics in Budapest, from May 27 to 31, 2019. Both the conference and this resulting volume are in honor of Professor András Némethi, on the occasion of his 60th birthday, whose work plays a decisive and influential role in the interactions between the above fields. The book should serve as a valuable resource for graduate students and researchers to deepen the new perspectives, methods, and connections between geometry and topology regarding singularities.

Author : José Seade
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 54,5 Mb
Release : 2005-11-18
Category : Mathematics
ISBN : 3764373229

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On the Topology of Isolated Singularities in Analytic Spaces by José Seade Pdf

This book has been awarded the Ferran Sunyer i Balaguer 2005 prize. The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology. The first chapters are mostly devoted to complex singularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor; the relation with 3-dimensional Lie groups; exotic spheres; spin structures and 3-manifold invariants; the geometry of quadrics and Arnold's theorem which states that the complex projective plane modulo conjugation is the 4-sphere. The second part of the book studies pioneer work about real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations. In the low dimensional case these turn out to be related to fibred links in the 3-sphere defined by meromorphic functions. This provides new methods for constructing manifolds equipped with a rich geometry. The book is largely self-contained and serves a wide audience of graduate students, mathematicians and researchers interested in geometry and topology.

Author : Christoph Lossen,Gerhard Pfister
Publisher : Cambridge University Press
Page : 412 pages
File Size : 43,5 Mb
Release : 2006-04-06
Category : Computers
ISBN : 0521683092

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Singularities and Computer Algebra by Christoph Lossen,Gerhard Pfister Pdf

A collection of articles giving overviews and open questions in singularities and their computational aspects.

Author : Alekseĭ Nikolaevich Khovanskiĭ
Publisher : American Mathematical Soc.
Page : 276 pages
File Size : 46,8 Mb
Release : 1997
Category : Geometry, Projective
ISBN : 0821808079

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Topics in Singularity Theory by Alekseĭ Nikolaevich Khovanskiĭ Pdf

Author : András Némethi,Ágnes Szilárd
Publisher : Springer
Page : 241 pages
File Size : 41,5 Mb
Release : 2012-01-05
Category : Mathematics
ISBN : 9783642236471

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Milnor Fiber Boundary of a Non-isolated Surface Singularity by András Némethi,Ágnes Szilárd Pdf

In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging non-isolated case. Let f be a complex analytic hypersurface germ in three variables whose zero set has a 1-dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber of f as an oriented plumbed 3-manifold. This method also provides the characteristic polynomial of the algebraic monodromy. We then determine the multiplicity system of the open book decomposition of M cut out by the argument of g for any complex analytic germ g such that the pair (f,g) is an ICIS. Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (f,g) are also described. The theory is supported by a substantial amount of examples, including homogeneous and composed singularities and suspensions. The properties peculiar to M are also emphasized.

Author : V. I. Arnold
Publisher : Cambridge University Press
Page : 277 pages
File Size : 51,8 Mb
Release : 1981-09-17
Category : Mathematics
ISBN : 9780521285117

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Singularity Theory by V. I. Arnold Pdf

Professor Arnold is a prolific and versatile mathematician who has done striking work in differential equations and geometrical aspects of analysis. In this volume are collected seven of his survey articles from Russian Mathematical Surveys on singularity theory, the area to which he has made most contribution. These surveys contain Arnold's own analysis and synthesis of a decade's work. All those interested in singularity theory will find this an invaluable compilation. Professor C. T. C. Wall has written an introduction outlining the significance and content of the articles.

Author : Luigi Rodino,M. W. Wong
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 42,5 Mb
Release : 2009-01-06
Category : Mathematics
ISBN : 9783764389697

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New Developments in Pseudo-Differential Operators by Luigi Rodino,M. W. Wong Pdf

This volume consists of peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held on August 13-18, 2007, and invited papers by experts in the field.

Author : David Bourqui,Johannes Nicaise,Julien Sebag
Publisher : World Scientific
Page : 312 pages
File Size : 53,9 Mb
Release : 2020-03-05
Category : Mathematics
ISBN : 9781786347213

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Arc Schemes And Singularities by David Bourqui,Johannes Nicaise,Julien Sebag Pdf

This title introduces the theory of arc schemes in algebraic geometry and singularity theory, with special emphasis on recent developments around the Nash problem for surfaces. The main challenges are to understand the global and local structure of arc schemes, and how they relate to the nature of the singularities on the variety. Since the arc scheme is an infinite dimensional object, new tools need to be developed to give a precise meaning to the notion of a singular point of the arc scheme.Other related topics are also explored, including motivic integration and dual intersection complexes of resolutions of singularities. Written by leading international experts, it offers a broad overview of different applications of arc schemes in algebraic geometry, singularity theory and representation theory.