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Author: José Luis Cisneros-Molina
Publisher: Springer Nature
ISBN: 3030780244
Category : Mathematics
Languages : en
Pages : 581
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Book Description
This is the second volume of the Handbook of the 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. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory and related topics. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and 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.
Author: José Luis Cisneros-Molina
Publisher: Springer Nature
ISBN: 3030780244
Category : Mathematics
Languages : en
Pages : 581
Get Book Here
Book Description
This is the second volume of the Handbook of the 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. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory and related topics. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and 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.
Author: Anthony Bahri
Publisher: Springer Nature
ISBN: 3031572041
Category :
Languages : en
Pages : 325
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Book Description
Author: José Luis Cisneros Molina
Publisher: Springer Nature
ISBN: 3030530612
Category : Mathematics
Languages : en
Pages : 616
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Book Description
This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. 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. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject. This is the first volume in 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. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Author: Santiago López de Medrano
Publisher: Springer Nature
ISBN: 3031283643
Category : Mathematics
Languages : en
Pages : 277
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Book Description
This book gives an overview of research in the topology and geometry of intersections of quadrics in $\mathbb{R}^n$, with a focus on intersections of concentric ellipsoids and related spaces. Unifying and organizing material previously spread over many articles, it also contains new results. The first part provides very detailed foundations of a wide-ranging theory that could be useful for future developments. It includes chapters on general intersections of quadrics, operations on them, and intersections of concentric and coaxial quadrics. Moving from the general to the specific, the second part focuses on a topological description of transverse intersections of concentric ellipsoids, including a complete description of the case of three ellipsoids, and of some large families of more than three of them. The third part looks at relations to other areas of mathematics such as dynamical systems, complex geometry, contact and symplectic geometry, and other applications. An appendix gathers some technical items and also gives an account of the origins, motivations and progression of the subject, including historical recollections of the author, who has been central to its development.
Author: Alexandru Dimca
Publisher: Springer Science & Business Media
ISBN: 1461244048
Category : Mathematics
Languages : en
Pages : 277
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Book Description
Author: Hans U. Boden
Publisher: American Mathematical Soc.
ISBN: 9780821871492
Category : Mathematics
Languages : en
Pages : 368
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Book Description
This book contains expository papers that give an up-to-date account of recent developments and open problems in the geometry and topology of manifolds, along with several research articles that present new results appearing in published form for the first time. The unifying theme is the problem of understanding manifolds in low dimensions, notably in dimensions three and four, and the techniques include algebraic topology, surgery theory, Donaldson and Seiberg-Witten gauge theory, Heegaard Floer homology, contact and symplectic geometry, and Gromov-Witten invariants. The articles collected for this volume were contributed by participants of the Conference "Geometry and Topology of Manifolds" held at McMaster University on May 14-18, 2004 and are representative of the many excellent talks delivered at the conference.
Author: José Luis Cisneros-Molina
Publisher: Springer
ISBN: 9783031687105
Category : Mathematics
Languages : en
Pages : 0
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Book Description
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.
Author: Demeter Krupka
Publisher: Elsevier
ISBN: 0080556736
Category : Mathematics
Languages : en
Pages : 1243
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Book Description
This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents
Author: Felipe Cano
Publisher: Springer
ISBN: 9783031524806
Category : Mathematics
Languages : en
Pages : 0
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Book Description
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.
Author: Athanase Papadopoulos
Publisher: Springer Nature
ISBN: 3031435109
Category :
Languages : en
Pages : 396
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Book Description
