Search Results: riemannian-holonomy-groups-and-calibrated-geometry-oxford-graduate-texts-in-mathematics

Riemannian Holonomy Groups and Calibrated Geometry

Author: Dominic D. Joyce

Publisher: Oxford University Press

ISBN: 019921560X

Category: Mathematics

Page: 303

View: 6242

Covering an exciting and active area of research at the crossroads of several different fields in mathematics and physics, and drawing on the author's previous work, this text has been written to explain the advanced mathematics involved simply and clearly to graduate students in both disciplines.

Cohomological Aspects in Complex Non-Kähler Geometry

Author: Daniele Angella

Publisher: Springer

ISBN: 3319024418

Category: Mathematics

Page: 262

View: 4380

In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kähler structure. On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kähler manifolds. On the other, in order to further investigate any of these properties, it is natural to look for manifolds that do not have any Kähler structure. We focus in particular on studying Bott-Chern and Aeppli cohomologies of compact complex manifolds. Several results concerning the computations of Dolbeault and Bott-Chern cohomologies on nilmanifolds are summarized, allowing readers to study explicit examples. Manifolds endowed with almost-complex structures, or with other special structures (such as, for example, symplectic, generalized-complex, etc.), are also considered.

Quantization, PDEs, and Geometry

The Interplay of Analysis and Mathematical Physics

Author: Dorothea Bahns,Wolfram Bauer,Ingo Witt

Publisher: Birkhäuser

ISBN: 3319224077

Category: Mathematics

Page: 314

View: 2836

This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability of solitary waves, and sub-Riemannian geometry. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen. The authors explain fundamental concepts and ideas and present them clearly. Starting from basic notions, these course notes take the reader to the point of current research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. All contributions are of interest to researchers in the respective fields, but they are also accessible to graduate students.

Supersymmetric Field Theories

Author: Sergio Cecotti

Publisher: Cambridge University Press

ISBN: 1107053811

Category: Science

Page: 424

View: 1930

Adopting an elegant geometrical approach, this advanced pedagogical text describes deep and intuitive methods for understanding the subtle logic of supersymmetry while avoiding lengthy computations. The book describes how complex results and formulae obtained using other approaches can be significantly simplified when translated to a geometric setting. Introductory chapters describe geometric structures in field theory in the general case, while detailed later chapters address specific structures such as parallel tensor fields, G-structures, and isometry groups. The relationship between structures in supergravity and periodic maps of algebraic manifolds, Kodaira-Spencer theory, modularity, and the arithmetic properties of supergravity are also addressed. Relevant geometric concepts are introduced and described in detail, providing a self-contained toolkit of useful techniques, formulae and constructions. Covering all the material necessary for the application of supersymmetric field theories to fundamental physical questions, this is an outstanding resource for graduate students and researchers in theoretical physics.

Vector Bundles and Complex Geometry

Conference on Vector Bundles in Honor of S. Ramanan on the Occasion of His 70th Birthday, June 16-20, 2008, Miraflores de la Sierra, Madrid, Spain

Author: S. Ramanan

Publisher: American Mathematical Soc.

ISBN: 0821847503

Category: Mathematics

Page: 206

View: 2613

This volume contains a collection of papers from the conference on Vector Bundles held at Miraflores de la sierra, Madrid, Spain on June 16-20, 2008, which honored S. Ramanan on his 70th birthday. The main areas covered in this volume are vector bundles, parabolic bundles, abelian varieties, hilbert schemes, contact structures, index theory, Hodge theory, and geometric invariant theory. Professor Ramanan has made important contributions in all of these areas.

Modern Geometry: A Celebration of the Work of Simon Donaldson

Author: Vicente Muñoz,Ivan Smith,Richard P. Thomas

Publisher: American Mathematical Soc.

ISBN: 1470440946

Category: Four-manifolds (Topology)

Page: 416

View: 6892

This book contains a collection of survey articles of exciting new developments in geometry, written in tribute to Simon Donaldson to celebrate his 60th birthday. Reflecting the wide range of Donaldson's interests and influence, the papers range from algebraic geometry and topology through symplectic geometry and geometric analysis to mathematical physics. Their expository nature means the book acts as an invitation to the various topics described, while also giving a sense of the links between these different areas and the unity of modern geometry.

Complex and Differential Geometry

Conference held at Leibniz Universität Hannover, September 14 – 18, 2009

Author: Wolfgang Ebeling,Klaus Hulek,Knut Smoczyk

Publisher: Springer Science & Business Media

ISBN: 9783642203008

Category: Mathematics

Page: 422

View: 3028

This volume contains the Proceedings of the conference "Complex and Differential Geometry 2009", held at Leibniz Universität Hannover, September 14 - 18, 2009. It was the aim of this conference to bring specialists from differential geometry and (complex) algebraic geometry together and to discuss new developments in and the interaction between these fields. Correspondingly, the articles in this book cover a wide area of topics, ranging from topics in (classical) algebraic geometry through complex geometry, including (holomorphic) symplectic and poisson geometry, to differential geometry (with an emphasis on curvature flows) and topology.

Topics in Several Complex Variables

Author: Zair Ibragimov,Norman Levenberg,Sergey Pinchuk,Azimbay Sadullaev

Publisher: American Mathematical Soc.

ISBN: 1470419270

Category: Functional analysis -- Topological linear spaces and related structures -- Graded Fraechet spaces and tame operators

Page: 156

View: 1171

This volume contains the proceedings of the Special Session on Several Complex Variables, which was held during the first USA-Uzbekistan Conference on Analysis and Mathematical Physics from May 20–23, 2014, at California State University, Fullerton. This volume covers a wide variety of topics in pluripotential theory, symplectic geometry and almost complex structures, integral formulas, holomorphic extension, and complex dynamics. In particular, the reader will find articles on Lagrangian submanifolds and rational convexity, multidimensional residues, S-parabolic Stein manifolds, Segre varieties, and the theory of quasianalytic functions.

Compact Manifolds with Special Holonomy

Author: Dominic D. Joyce

Publisher: Oxford University Press on Demand

ISBN: 9780198506010

Category: Mathematics

Page: 436

View: 5364

This is a combination of a graduate textbook on Riemannian holonomy groups, and a research monograph on compact manifolds with the exceptional holonomy groups G2 and Spin (7). It is the first book on compact manifolds with exceptional holonomy, and contains much new research material and many new examples.

Spin Geometry (PMS-38)

Author: H. Blaine Lawson,Marie-Louise Michelsohn

Publisher: Princeton University Press

ISBN: 1400883911

Category: Mathematics

Page: 440

View: 6852

This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration. A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds.

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 5560

Introduction to Banach Spaces and Algebras

Author: Graham R. Allan,Harold G. Dales

Publisher: Oxford University Press

ISBN: 0199206538

Category: Banach algebras

Page: 371

View: 2404

A graduate level text in functional analysis, with an emphasis on Banach algebras. Based on lectures given for Part III of the Cambridge Mathematical Tripos, the text will assume a familiarity with elementary real and complex analysis, and some acquaintance with metric spaces, analytic topology and normed spaces (but not theorems depending on Baire category, or any version of the Hahn-Banach theorem).

Complex Geometry

An Introduction

Author: Daniel Huybrechts

Publisher: Springer Science & Business Media

ISBN: 3540266879

Category: Mathematics

Page: 309

View: 3258

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

Stochastic Analysis and Diffusion Processes

Author: Gopinath Kallianpur,P Sundar

Publisher: Oxford University Press

ISBN: 0199657076

Category: Mathematics

Page: 352

View: 349

Beginning with the concept of random processes and Brownian motion and building on the theory and research directions in a self-contained manner, this book provides an introduction to stochastic analysis for graduate students, researchers and applied scientists interested in stochastic processes and their applications.

Calabi-Yau Manifolds and Related Geometries

Lectures at a Summer School in Nordfjordeid, Norway, June 2001

Author: Mark Gross,Daniel Huybrechts,Dominic Joyce

Publisher: Springer Science & Business Media

ISBN: 3642190049

Category: Mathematics

Page: 244

View: 9271

This is an introduction to a very active field of research, on the boundary between mathematics and physics. It is aimed at graduate students and researchers in geometry and string theory. Proofs or sketches are given for many important results. From the reviews: "An excellent introduction to current research in the geometry of Calabi-Yau manifolds, hyper-Kähler manifolds, exceptional holonomy and mirror symmetry....This is an excellent and useful book." --MATHEMATICAL REVIEWS

Lie Groups and Lie Algebras - A Physicist's Perspective

Author: Adam M. Bincer

Publisher: Oxford University Press

ISBN: 0199662924

Category: Mathematics

Page: 201

View: 5654

This book is intended for graduate students in Physics, especially Elementary Particle Physics. It gives an introduction to group theory for physicists with a focus on Lie groups and Lie algebras.

Surveys on geometry and integrable systems

Author: Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita

Publisher: Amer Mathematical Society

ISBN: N.A

Category: Mathematics

Page: 510

View: 2932

Introduction to Symplectic Topology

Author: Dusa McDuff,Dietmar Salamon

Publisher: Oxford University Press

ISBN: 0198794894

Category: Mathematics

Page: 632

View: 7264

Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. A significantly revised second edition was published in 1998 introducing new sections and updates on the fast-developing area. This new third edition includes updates and new material to bring the book right up-to-date.

Hyperbolic Dynamics and Brownian Motion

An Introduction

Author: Jacques Franchi,Yves Le Jan

Publisher: Oxford University Press

ISBN: 0199654107

Category: Mathematics

Page: 266

View: 9788

A simple introduction to several important fields of modern mathematics. The exposition is based on an interplay between hyperbolic geometry, stochastic calculus, special relativity and chaotic dynamics. It is suitable for anyone with some solid background in linear algebra, calculus, and probability theory.

Matroid Theory

AMS-IMS-SIAM Joint Summer Research Conference on Matroid Theory, July 2-6, 1995, University of Washington, Seattle

Author: Joseph Edmond Bonin

Publisher: American Mathematical Soc.

ISBN: 0821805088

Category: Mathematics

Page: 418

View: 1921

This volume contains the proceedings of the 1995 AMS-IMS-SIAM Joint Summer Research Conference on Matroid Theory held at the University of Washington, Seattle. The book features three comprehensive surveys that bring the reader to the forefront of research in matroid theory. Joseph Kung's encyclopedic treatment of the critical problem traces the development of this problem from its origins through its numerous links with other branches of mathematics to the current status of its many aspects. James Oxley's survey of the role of connectivity and structure theorems in matroid theory stresses the influence of the Wheels and Whirls Theorem of Tutte and the Splitter Theorem of Seymour. Walter Whiteley's article unifies applications of matroid theory to constrained geometrical systems, including the rigidity of bar-and-joint frameworks, parallel drawings, and splines. These widely accessible articles contain many new results and directions for further research and applications. The surveys are complemented by selected short research papers. The volume concludes with a chapter of open problems. Features self-contained, accessible surveys of three active research areas in matroid theory; many new results; pointers to new research topics; a chapter of open problems; mathematical applications; and applications and connections to other disciplines, such as computer-aided design and electrical and structural engineering.

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