Calabi-Yau Manifolds and Related Geometries
Title | Calabi-Yau Manifolds and Related Geometries PDF eBook |
Author | Mark Gross |
Publisher | Springer Science & Business Media |
Pages | 245 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3642190049 |
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
Calabi-Yau Varieties and Mirror Symmetry
Title | Calabi-Yau Varieties and Mirror Symmetry PDF eBook |
Author | Noriko Yui |
Publisher | American Mathematical Soc. |
Pages | 385 |
Release | 2003 |
Genre | Mathematics |
ISBN | 0821833553 |
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.
Riemannian Holonomy Groups and Calibrated Geometry
Title | Riemannian Holonomy Groups and Calibrated Geometry PDF eBook |
Author | Dominic D. Joyce |
Publisher | Oxford University Press |
Pages | 314 |
Release | 2007 |
Genre | Mathematics |
ISBN | 019921560X |
Riemannian Holonomy Groups and Calibrated Geometry covers an exciting and active area of research at the crossroads of several different fields in mathematics and physics. Drawing on the author's previous work the text has been written to explain the advanced mathematics involved simply and clearly to graduate students in both disciplines.
The Calabi–Yau Landscape
Title | The Calabi–Yau Landscape PDF eBook |
Author | Yang-Hui He |
Publisher | Springer Nature |
Pages | 214 |
Release | 2021-07-31 |
Genre | Mathematics |
ISBN | 3030775623 |
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.
Calabi-Yau Manifolds a Bestiary for Physicists
Title | Calabi-Yau Manifolds a Bestiary for Physicists PDF eBook |
Author | Tristan Hübsch |
Publisher | World Scientific Publishing Company Incorporated |
Pages | 362 |
Release | 1992 |
Genre | Science |
ISBN | 9789810206628 |
From the author's preface: "New manifolds are being created every moment, joining the menagerie . . . Our task therefore becomes taxonomy in part, guiding the interested reader through the web of known Calabi-Yau manifolds and preparing the more adventurous reader for a voyage into the jungle with many more beasts to be discovered." The focus is on techniques and methods which will have long-lasting application. Acidic paper. Annotation copyrighted by Book News, Inc., Portland, OR
Modular Calabi-Yau Threefolds
Title | Modular Calabi-Yau Threefolds PDF eBook |
Author | Christian Meyer |
Publisher | American Mathematical Soc. |
Pages | 207 |
Release | 2005 |
Genre | Mathematics |
ISBN | 082183908X |
"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."--Jaquette.
Calabi-Yau Manifolds
Title | Calabi-Yau Manifolds PDF eBook |
Author | Tristan Hbsch |
Publisher | World Scientific |
Pages | 383 |
Release | 1994 |
Genre | Science |
ISBN | 981021927X |
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.