The Calabi Yau Landscape

Author : Yang-Hui He
Publisher : Springer Nature
Page : 214 pages
File Size : 41,8 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 : Yang-Hui He
Publisher : Unknown
Page : 0 pages
File Size : 51,8 Mb
Release : 2021
Category : Electronic
ISBN : 3030775631

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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 : Arthur Hebecker
Publisher : Springer Nature
Page : 321 pages
File Size : 51,9 Mb
Release : 2021-03-26
Category : Science
ISBN : 9783030651510

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Naturalness, String Landscape and Multiverse by Arthur Hebecker Pdf

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.

Author : Shing-Tung Yau,Steven J. Nadis
Publisher : Il Saggiatore
Page : 398 pages
File Size : 55,6 Mb
Release : 2010-09-07
Category : Mathematics
ISBN : 9780465020232

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The Shape of Inner Space by Shing-Tung Yau,Steven J. Nadis Pdf

The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.

Author : Yang-hui He
Publisher : World Scientific
Page : 418 pages
File Size : 52,8 Mb
Release : 2023-06-21
Category : Computers
ISBN : 9781800613713

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Machine Learning In Pure Mathematics And Theoretical Physics by Yang-hui He Pdf

The juxtaposition of 'machine learning' and 'pure mathematics and theoretical physics' may first appear as contradictory in terms. The rigours of proofs and derivations in the latter seem to reside in a different world from the randomness of data and statistics in the former. Yet, an often under-appreciated component of mathematical discovery, typically not presented in a final draft, is experimentation: both with ideas and with mathematical data. Think of the teenage Gauss, who conjectured the Prime Number Theorem by plotting the prime-counting function, many decades before complex analysis was formalized to offer a proof.Can modern technology in part mimic Gauss's intuition? The past five years saw an explosion of activity in using AI to assist the human mind in uncovering new mathematics: finding patterns, accelerating computations, and raising conjectures via the machine learning of pure, noiseless data. The aim of this book, a first of its kind, is to collect research and survey articles from experts in this emerging dialogue between theoretical mathematics and machine learning. It does not dwell on the well-known multitude of mathematical techniques in deep learning, but focuses on the reverse relationship: how machine learning helps with mathematics. Taking a panoramic approach, the topics range from combinatorics to number theory, and from geometry to quantum field theory and string theory. Aimed at PhD students as well as seasoned researchers, each self-contained chapter offers a glimpse of an exciting future of this symbiosis.

Author : Vladimir Dobrev
Publisher : Springer Nature
Page : 526 pages
File Size : 42,6 Mb
Release : 2023-01-29
Category : Mathematics
ISBN : 9789811947513

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Lie Theory and Its Applications in Physics by Vladimir Dobrev Pdf

This volume presents modern trends in the area of symmetries and their applications based on contributions to the Workshop "Lie Theory and Its Applications in Physics" held in Sofia, Bulgaria (on-line) in June 2021. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a big interdisciplinary and interrelated field. The topics covered in this Volume are the most modern trends in the field of the Workshop: Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, Exceptional quantum algebra for the standard model of particle physics, Gauge Theories and Applications, Structures on Lie Groups and Lie Algebras. This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Author : Sergio Cecotti
Publisher : Springer Nature
Page : 846 pages
File Size : 48,6 Mb
Release : 2023-11-07
Category : Science
ISBN : 9783031365300

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Introduction to String Theory by Sergio Cecotti Pdf

Graduate students typically enter into courses on string theory having little to no familiarity with the mathematical background so crucial to the discipline. As such, this book, based on lecture notes, edited and expanded, from the graduate course taught by the author at SISSA and BIMSA, places particular emphasis on said mathematical background. The target audience for the book includes students of both theoretical physics and mathematics. This explains the book’s "strange" style: on the one hand, it is highly didactic and explicit, with a host of examples for the physicists, but, in addition, there are also almost 100 separate technical boxes, appendices, and starred sections, in which matters discussed in the main text are put into a broader mathematical perspective, while deeper and more rigorous points of view (particularly those from the modern era) are presented. The boxes also serve to further shore up the reader’s understanding of the underlying math. In writing this book, the author’s goal was not to achieve any sort of definitive conciseness, opting instead for clarity and "completeness". To this end, several arguments are presented more than once from different viewpoints and in varying contexts.

Author : Anonim
Publisher : Elsevier
Page : 260 pages
File Size : 41,5 Mb
Release : 2023-09-01
Category : Mathematics
ISBN : 9780443137648

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Artificial Intelligence by Anonim Pdf

Artificial Intelligence, Volume 49 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics. Chapters in this new release include AI Teacher-Student based Adaptive Structural Deep Learning Model and Its Estimating Uncertainty of Image Data, Machine-derived Intelligence: Computations Beyond the Null Hypothesis, Object oriented basis of artificial intelligence methodologies I in Judicial Systems in India, Artificial Intelligence in Systems Biology, Machine-Learning in Geometry and Physics, Innovation and Machine Learning: Crowdsourcing Open-Source Natural Language Processing (NLP) Algorithms to Advance Public Health Surveillance, and more. Other chapters cover Learning and identity testing of Markov chains, Data privacy for machine learning and statistics, and The interface between AI and Mathematics. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Statistics series Includes the latest information on Artificial Intelligence

Author : Volker Knecht
Publisher : CRC Press
Page : 147 pages
File Size : 45,9 Mb
Release : 2022-08-29
Category : Computers
ISBN : 9781000643831

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AI for Physics by Volker Knecht Pdf

Written in accessible language without mathematical formulas, this short book provides an overview of the wide and varied applications of artificial intelligence (AI) across the spectrum of physical sciences. Focusing in particular on AI's ability to extract patterns from data, known as machine learning (ML), the book includes a chapter on important machine learning algorithms and their respective applications in physics. It then explores the use of ML across a number of important sub-fields in more detail, ranging from particle, molecular and condensed matter physics, to astrophysics, cosmology and the theory of everything. The book covers such applications as the search for new particles and the detection of gravitational waves from the merging of black holes, and concludes by discussing what the future may hold.

Author : Frank Nielsen
Publisher : Springer Nature
Page : 274 pages
File Size : 45,7 Mb
Release : 2021-03-14
Category : Science
ISBN : 9783030654597

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Progress in Information Geometry by Frank Nielsen Pdf

This book focuses on information-geometric manifolds of structured data and models and related applied mathematics. It features new and fruitful interactions between several branches of science: Advanced Signal/Image/Video Processing, Complex Data Modeling and Analysis, Statistics on Manifolds, Topology/Machine/Deep Learning and Artificial Intelligence. The selection of applications makes the book a substantial information source, not only for academic scientist but it is also highly relevant for industry. The book project was initiated following discussions at the international conference GSI’2019 – Geometric Science of Information that was held at ENAC, Toulouse (France).

Author : Matti Pitkanen
Publisher : Bentham Science Publishers
Page : 1235 pages
File Size : 40,5 Mb
Release : 2016-03-03
Category : Science
ISBN : 9781681081793

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Topological Geometrodynamics by Matti Pitkanen Pdf

Topological geometrodynamics (TGD) is a modification of the theory of general relativity inspired by the problems related to the definition of inertial and gravitational energies in the earlier hypotheses. TGD is also a generalization of super string models. TGD brings forth an elegant theoretical projection of reality and builds upon the work by renowned scientists (Wheeler, Feynman, Penrose, Einstein, Josephson to name a few). In TGD, Physical space-time planes are visualized as four-dimensional surfaces in a certain 8-dimensional space (H). The choice of H is fixed by symmetries of standard model and leads to a geometric mapping of known classical fields and elementary particle numbers. TGD differs from Einstein’s geometrodynamics in the way space-time planes or ‘sheets’ are lumped together. Extending the theory based on fusing number concepts implies a further generalisation of the space-time concept allowing the identification of space-time correlates of cognition and intentionality. Additionally, zero energy ontology forces an extension of quantum measurement theory to a theory of consciousness and a hierarchy of phases is identified. Dark matter is thus predicted with far reaching implications for the understanding of consciousness and living systems. Therefore, it sets a solid foundation for modeling our universe in geometric terms. Topological Geometrodynamics: An Overview explains basic and advanced concepts about TGD. The book covers introductory information and classical TGD concepts before delving into twistor-space theory, particle physics, infinite-dimensional spinor geometry, generalized number theory, Planck constants, and the applications of TGD theory in research. The book is a valuable guide to TDG theory for researchers and advanced graduates in theoretical physics and cosmology.

Author : Leonard Susskind
Publisher : Back Bay Books
Page : 416 pages
File Size : 45,9 Mb
Release : 2008-12-14
Category : Science
ISBN : 9780316055581

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The Cosmic Landscape by Leonard Susskind Pdf

In his first book ever, the father of string theory reinvents the world's concept of the known universe and man's unique place within it. Line drawings.

Author : K. Bharatdwaj
Publisher : Discovery Publishing House
Page : 320 pages
File Size : 46,6 Mb
Release : 2009
Category : Physical geography
ISBN : 8183564410

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Physical Geography: a Landscape Appreciations by K. Bharatdwaj Pdf

Author : Peter Andreyevich
Publisher : Andrzej Horodeński
Page : 77 pages
File Size : 47,7 Mb
Release : 2015-03-22
Category : Electronic
ISBN : 8210379456XXX

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God Under Investigation by Peter Andreyevich Pdf

Looking for direct intellectual access to God by scientific means is rather doomed to fail. Yet, we have a right to check if man, in their scientific investigations, has not come close to such borders of cognition beyond which one can see areas which do not belong to cognizable world, usually defined as metaphysical, transcendental or spiritual. If we find such a place, this is as if we knocked on God's window. In his search for plausible ways to this window, the Author analyzes extensive evidence with reference to quantum mechanics, theory of relativity, theory of evolution, genetics and cognitive science. Of course, any attempt to give an objective verdict must lead to a catastrophe. But, what really matters is not a verdict but the fact that the investigation continues. The book will be enjoyed by all those who have capacity to reflect upon the key philosophical question: why is there something rather than nothing? ========= If you think this book is worth of reading you can confirm this opinion with the use of the bank account: PL07249000050000400057303247 (USD) ;)

Author : Jim Baggott
Publisher : Simon and Schuster
Page : 471 pages
File Size : 42,9 Mb
Release : 2021-11-15
Category : Science
ISBN : 9781639360383

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Farewell to Reality by Jim Baggott Pdf

From acclaimed science author Jim Baggot, a lively, provocative, and “intellectually gratifying” critique of modern theoretical physics (The Economist). In this stunning new volume, Jim Baggott argues that there is no observational or experimental evidence for many of the ideas of modern theoretical physics: super-symmetric particles, superstrings, the multiverse, the holographic principle, or the anthropic cosmological principle. These theories are not only untrue, it is not even science. It is fairy-tale physics: fantastical, bizarre and often outrageous, perhaps even confidence-trickery. This book provides a much-needed antidote. Informed, comprehensive, and balanced, it offers lay readers the latest ideas about the nature of physical reality while clearly distinguishing between fact and fantasy. With its engaging portraits of many central figures of modern physics, including Paul Davies, John Barrow, Brian Greene, Stephen Hawking, and Leonard Susskind, it promises to be essential reading for all readers interested in what we know and don''''t know about the nature of the universe and reality itself.