Calabi Yau Manifolds And Related Geometries

Author : Mark Gross,Daniel Huybrechts,Dominic Joyce
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642190049

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Calabi-Yau Manifolds and Related Geometries by Mark Gross,Daniel Huybrechts,Dominic Joyce Pdf

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

Author : Tristan Hbsch
Publisher : World Scientific
Page : 383 pages
File Size : 43,6 Mb
Release : 1994
Category : Science
ISBN : 9789810219277

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Calabi-Yau Manifolds by Tristan Hbsch Pdf

Calabi-Yau spaces are complex spaces with a vanishing first Chern class, or equivalently, with trivial canonical bundle (canonical class). They are used to construct possibly realistic (super)string models and are thus being studied vigorously in the recent physics literature.In the main part of the Book, collected and reviewed are relevant results on (1) several major techniques of constructing such spaces and (2) computation of physically relevant quantities such as massless field spectra and their Yukawa interactions. Issues of (3) stringy corrections and (4) moduli space and its geometry are still in the stage of rapid and continuing development, whence there is more emphasis on open problems here. Also is included a preliminary discussion of the conjectured universal moduli space and related open problems. Finally, several detailed models and sample computations are included throughout the Book to exemplify the techniques and the general discussion.The Book also contains a Lexicon (28 pages) of 150 assorted terms, key-words and main results and theorems, well suited for a handy reference. Although cross-referenced with the main part of the Book, the Lexicon can also be used independently.The level of mathematics is guided and developed between that of the popular Physics Reports of Eguchi, Gilkey and Hanson and the book Superstrings (Vol. 2) by Green, Schwarz and Witten on one end and Principles of Algebraic Geometry of Griffiths and Harris on the other.This is the first systematic exposition in book form of the material on Calabi-Yau spaces, related mathematics and the physics application, otherwise scattered through research articles in journals and conference proceedings.

Author : Radu Laza,Matthias Schütt,Noriko Yui
Publisher : Springer Science & Business Media
Page : 613 pages
File Size : 45,7 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781461464037

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Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds by Radu Laza,Matthias Schütt,Noriko Yui Pdf

In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the big variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with 3 days of introductory lectures. A selection of 4 of these lectures is included in this volume. These lectures can be used as a starting point for the graduate students and other junior researchers, or as a guide to the subject.

Author : Noriko Yui,James Dominic Lewis
Publisher : American Mathematical Soc.
Page : 385 pages
File Size : 51,7 Mb
Release : 2003
Category : Calabi-Yau manifolds
ISBN : 9780821833551

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Calabi-Yau Varieties and Mirror Symmetry by Noriko Yui,James Dominic Lewis Pdf

The idea of mirror symmetry originated in physics, but in recent years, the field of mirror symmetry has exploded onto the mathematical scene. It has inspired many new developments in algebraic and arithmetic geometry, toric geometry, the theory of Riemann surfaces, and infinite-dimensional Lie algebras among others. The developments in physics stimulated the interest of mathematicians in Calabi-Yau varieties. This led to the realization that the time is ripe for mathematicians, armed with many concrete examples and alerted by the mirror symmetry phenomenon, to focus on Calabi-Yau varieties and to test for these special varieties some of the great outstanding conjectures, e.g., the modularity conjecture for Calabi-Yau threefolds defined over the rationals, the Bloch-Beilinson conjectures, regulator maps of higher algebraic cycles, Picard-Fuchs differential equations, GKZ hypergeometric systems, and others. The articles in this volume report on current developments. The papers are divided roughly into two categories: geometric methods and arithmetic methods. One of the significant outcomes of the workshop is that we are finally beginning to understand the mirror symmetry phenomenon from the arithmetic point of view, namely, in terms of zeta-functions and L-series of mirror pairs of Calabi-Yau threefolds. The book is suitable for researchers interested in mirror symmetry and string theory.

Author : Dominic D. Joyce
Publisher : Oxford University Press
Page : 314 pages
File Size : 55,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9780199215607

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Riemannian Holonomy Groups and Calibrated Geometry by Dominic D. Joyce Pdf

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.

Author : Christian Rohde
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 50,9 Mb
Release : 2009-04-28
Category : Mathematics
ISBN : 9783642006388

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Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication by Christian Rohde Pdf

The main goal of this book is the construction of families of Calabi-Yau 3-manifolds with dense sets of complex multiplication fibers. The new families are determined by combining and generalizing two methods. Firstly, the method of E. Viehweg and K. Zuo, who have constructed a deformation of the Fermat quintic with a dense set of CM fibers by a tower of cyclic coverings. Using this method, new families of K3 surfaces with dense sets of CM fibers and involutions are obtained. Secondly, the construction method of the Borcea-Voisin mirror family, which in the case of the author's examples yields families of Calabi-Yau 3-manifolds with dense sets of CM fibers, is also utilized. Moreover fibers with complex multiplication of these new families are also determined. This book was written for young mathematicians, physicists and also for experts who are interested in complex multiplication and varieties with complex multiplication. The reader is introduced to generic Mumford-Tate groups and Shimura data, which are among the main tools used here. The generic Mumford-Tate groups of families of cyclic covers of the projective line are computed for a broad range of examples.

Author : Radu Laza,Matthias Schütt,Noriko Yui
Publisher : Springer
Page : 547 pages
File Size : 54,7 Mb
Release : 2015-08-27
Category : Mathematics
ISBN : 9781493928309

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Calabi-Yau Varieties: Arithmetic, Geometry and Physics by Radu Laza,Matthias Schütt,Noriko Yui Pdf

This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.

Author : P. de Bartolomeis,F. Tricerri,E. Vesentini
Publisher : Cambridge University Press
Page : 336 pages
File Size : 44,6 Mb
Release : 1996-06-13
Category : Mathematics
ISBN : 0521562163

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Manifolds and Geometry by P. de Bartolomeis,F. Tricerri,E. Vesentini Pdf

This book brings together papers that cover a wide spectrum of areas and give an unsurpassed overview of research into differential geometry.

Author : Yang Li
Publisher : American Mathematical Society
Page : 138 pages
File Size : 48,5 Mb
Release : 2024-01-26
Category : Mathematics
ISBN : 9781470467821

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SYZ Geometry for Calabi-Yau 3-folds: Taub-NUT and Ooguri-Vafa Type Metrics by Yang Li Pdf

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Author : Yang-Hui He
Publisher : Springer Nature
Page : 214 pages
File Size : 41,7 Mb
Release : 2021-07-31
Category : Mathematics
ISBN : 9783030775629

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The Calabi–Yau Landscape by Yang-Hui He Pdf

Can artificial intelligence learn mathematics? The question is at the heart of this original monograph bringing together theoretical physics, modern geometry, and data science. The study of Calabi–Yau manifolds lies at an exciting intersection between physics and mathematics. Recently, there has been much activity in applying machine learning to solve otherwise intractable problems, to conjecture new formulae, or to understand the underlying structure of mathematics. In this book, insights from string and quantum field theory are combined with powerful techniques from complex and algebraic geometry, then translated into algorithms with the ultimate aim of deriving new information about Calabi–Yau manifolds. While the motivation comes from mathematical physics, the techniques are purely mathematical and the theme is that of explicit calculations. The reader is guided through the theory and provided with explicit computer code in standard software such as SageMath, Python and Mathematica to gain hands-on experience in applications of artificial intelligence to geometry. Driven by data and written in an informal style, The Calabi–Yau Landscape makes cutting-edge topics in mathematical physics, geometry and machine learning readily accessible to graduate students and beyond. The overriding ambition is to introduce some modern mathematics to the physicist, some modern physics to the mathematician, and machine learning to both.

Author : Andrei Moroianu
Publisher : Cambridge University Press
Page : 4 pages
File Size : 43,5 Mb
Release : 2007-03-29
Category : Mathematics
ISBN : 9781139463003

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Lectures on Kähler Geometry by Andrei Moroianu Pdf

Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi–Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.

Author : David A. Cox,Sheldon Katz
Publisher : American Mathematical Soc.
Page : 469 pages
File Size : 55,7 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821821275

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Mirror Symmetry and Algebraic Geometry by David A. Cox,Sheldon Katz Pdf

Mathematicians wanting to get into the field ... will find a very well written and encyclopaedic account of the mathematics which was needed in, and was developed from, what now might be termed classical mirror symmetry. --Bulletin of the LMS The book is highly recommended for everyone who wants to learn about the fascinating recent interplay between physics and mathematics. --Mathematical Reviews Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in four-dimensional projective space. Understanding the mathematics behind these predictions has been a substantial challenge. This book is a completely comprehensive monograph on mirror symmetry, covering the original observations by the physicists through the most recent progress made to date. Subjects discussed include toric varieties, Hodge theory, Kahler geometry, moduli of stable maps, Calabi-Yau manifolds, quantum cohomology, Gromov-Witten invariants, and the mirror theorem.

Author : Spiro Karigiannis,Naichung Conan Leung,Jason D. Lotay
Publisher : Springer Nature
Page : 392 pages
File Size : 41,9 Mb
Release : 2020-05-26
Category : Mathematics
ISBN : 9781071605776

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Lectures and Surveys on G2-Manifolds and Related Topics by Spiro Karigiannis,Naichung Conan Leung,Jason D. Lotay Pdf

This book, one of the first on G2 manifolds in decades, collects introductory lectures and survey articles largely based on talks given at a workshop held at the Fields Institute in August 2017, as part of the major thematic program on geometric analysis. It provides an accessible introduction to various aspects of the geometry of G2 manifolds, including the construction of examples, as well as the intimate relations with calibrated geometry, Yang-Mills gauge theory, and geometric flows. It also features the inclusion of a survey on the new topological and analytic invariants of G2 manifolds that have been recently discovered. The first half of the book, consisting of several introductory lectures, is aimed at experienced graduate students or early career researchers in geometry and topology who wish to familiarize themselves with this burgeoning field. The second half, consisting of numerous survey articles, is intended to be useful to both beginners and experts in the field.

Author : Radu Laza,Matthias Schutt,Noriko Yui
Publisher : Unknown
Page : 630 pages
File Size : 50,8 Mb
Release : 2013-07-31
Category : Electronic
ISBN : 1461464048

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Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds by Radu Laza,Matthias Schutt,Noriko Yui Pdf

Author : Christian Meyer
Publisher : American Mathematical Soc.
Page : 207 pages
File Size : 46,8 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821839089

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Modular Calabi-Yau Threefolds by Christian Meyer Pdf

The main subject of this book is the connection between Calabi-Yau threefolds and modular forms. The book presents the general theory and brings together the known results. It studies hundreds of new examples of rigid and non-rigid modular Calabi-Yau threefolds and correspondences between them. Conjectures about the possible levels of modular forms connected with Calabi-Yau threefolds are presented. Tables of newforms of weight four and large levels are compiled and included in the appendix.