Calabi-Yau Varieties: Arithmetic, Geometry and Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Calabi-Yau Varieties: Arithmetic, Geometry and Physics write by Radu Laza. This book was released on 2015-08-27. Calabi-Yau Varieties: Arithmetic, Geometry and Physics available in PDF, EPUB and Kindle. 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.
Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds
Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds write by Radu Laza. This book was released on 2013-06-12. Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds available in PDF, EPUB and Kindle. 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.
Calabi-Yau Varieties and Mirror Symmetry
Calabi-Yau Varieties and Mirror Symmetry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Calabi-Yau Varieties and Mirror Symmetry write by Noriko Yui. This book was released on 2003. Calabi-Yau Varieties and Mirror Symmetry available in PDF, EPUB and Kindle. 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.
Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds
Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds write by Radu Laza. This book was released on 2013-07-31. Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds available in PDF, EPUB and Kindle.
The Calabi–Yau Landscape
The Calabi–Yau Landscape - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Calabi–Yau Landscape write by Yang-Hui He. This book was released on 2021-07-31. The Calabi–Yau Landscape available in PDF, EPUB and Kindle. 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.
