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.
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. 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.
The Shape of Inner Space
The Shape of Inner Space - 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 Shape of Inner Space write by Shing-Tung Yau. This book was released on 2010-09-07. The Shape of Inner Space available in PDF, EPUB and Kindle. The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.
Naturalness, String Landscape and Multiverse
Naturalness, String Landscape and Multiverse - 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 Naturalness, String Landscape and Multiverse write by Arthur Hebecker. This book was released on 2021-03-26. Naturalness, String Landscape and Multiverse available in PDF, EPUB and Kindle. This book presents a string-theoretic approach to new ideas in particle physics, also known as Physics Beyond the Standard Model, and to cosmology. The concept of Naturalness and its apparent violation by the low electroweak scale and the small cosmological constant is emphasized. It is shown that string theory, through its multitude of solutions, known as the landscape, offers a partial resolution to these naturalness problems as well as suggesting more speculative possibilities like that of a multiverse. The book is based on a one-semester course, as such, it has a pedagogical approach, is self-contained and includes many exercises with solutions. Notably, the basics of string theory are introduced as part of the lectures. These notes are aimed at graduate students with a solid background in quantum field theory, as well as at young researchers from theoretical particle physics to mathematical physics. This text also benefits students who are in the process of studying string theory at a deeper level. In this case, the volume serves as additional reading beyond a formal string theory course.
Calabi-Yau Manifolds
Calabi-Yau Manifolds - 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 Manifolds write by Tristan Hbsch. This book was released on 1994. Calabi-Yau Manifolds available in PDF, EPUB and Kindle. 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.
