Q Stability Conditions Via Q Quadratic Differentials For Calabi Yau Mathbb X Categories
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Q Stability Conditions Via Q Quadratic Differentials For Calabi Yau Mathbb X Categories
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Author : Akishi Ikeda
language : en
Publisher: American Mathematical Society
Release Date : 2025-05-29
Q Stability Conditions Via Q Quadratic Differentials For Calabi Yau Mathbb X Categories written by Akishi Ikeda and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-29 with Mathematics categories.
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Lectures On K3 Surfaces
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Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2016-09-26
Lectures On K3 Surfaces written by Daniel Huybrechts and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-26 with Mathematics categories.
Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.
Homological Mirror Symmetry And Tropical Geometry
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Author : Ricardo Castano-Bernard
language : en
Publisher: Springer
Release Date : 2014-10-16
Homological Mirror Symmetry And Tropical Geometry written by Ricardo Castano-Bernard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-16 with Mathematics categories.
The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Geometry studies piecewise-linear objects which appear as “degenerations” of the corresponding algebro-geometric objects.
The Calabi Yau Landscape
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Author : Yang-Hui He
language : en
Publisher: Springer Nature
Release Date : 2021-07-31
The Calabi Yau Landscape written by Yang-Hui He and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-31 with Mathematics categories.
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.
An Introduction To Two Dimensional Quantum Field Theory With 0 2 Supersymmetry
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Author : Ilarion V. Melnikov
language : en
Publisher: Springer
Release Date : 2019-02-11
An Introduction To Two Dimensional Quantum Field Theory With 0 2 Supersymmetry written by Ilarion V. Melnikov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-11 with Science categories.
This book introduces two-dimensional supersymmetric field theories with emphasis on both linear and non-linear sigma models. Complex differential geometry, in connection with supersymmetry, has played a key role in most developments of the last thirty years in quantum field theory and string theory. Both structures introduce a great deal of rigidity compared to the more general categories of non-supersymmetric theories and real differential geometry, allowing for many general conceptual results and detailed quantitative predictions. Two-dimensional (0,2) supersymmetric quantum field theories provide a natural arena for the fruitful interplay between geometry and quantum field theory. These theories play an important role in string theory and provide generalizations, still to be explored fully, of rich structures such as mirror symmetry. They also have applications to non-perturbative four-dimensional physics, for instance as descriptions of surface defects or low energy dynamics of solitonic strings in four-dimensional supersymmetric theories. The purpose of these lecture notes is to acquaint the reader with these fascinating theories, assuming a background in conformal theory, quantum field theory and differential geometry at the beginning graduate level. In order to investigate the profound relations between structures from complex geometry and field theory the text begins with a thorough examination of the basic structures of (0,2) quantum field theory and conformal field theory. Next, a simple class of Lagrangian theories, the (0,2) Landau-Ginzburg models, are discussed, together with the resulting renormalization group flows, dynamics, and symmetries. After a thorough introduction and examination of (0,2) non-linear sigma models, the text introduces linear sigma models that, in particular, provide a unified treatment of non-linear sigma models and Landau-Ginzburg theories. Many exercises, along with discussions of relevant mathematical notions and important open problems in the field, are included in the text.
Advances In Geometry And Lie Algebras From Supergravity
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Author : Pietro Giuseppe Frè
language : en
Publisher: Springer
Release Date : 2018-02-24
Advances In Geometry And Lie Algebras From Supergravity written by Pietro Giuseppe Frè and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-24 with Science categories.
This book aims to provide an overview of several topics in advanced differential geometry and Lie group theory, all of them stemming from mathematical problems in supersymmetric physical theories. It presents a mathematical illustration of the main development in geometry and symmetry theory that occurred under the fertilizing influence of supersymmetry/supergravity. The contents are mainly of mathematical nature, but each topic is introduced by historical information and enriched with motivations from high energy physics, which help the reader in getting a deeper comprehension of the subject.
Abelian Varieties Theta Functions And The Fourier Transform
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Author : Alexander Polishchuk
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-21
Abelian Varieties Theta Functions And The Fourier Transform written by Alexander Polishchuk and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-21 with Mathematics categories.
Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.
Complex Non K Hler Geometry
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Author : Sławomir Dinew
language : en
Publisher: Springer Nature
Release Date : 2019-11-05
Complex Non K Hler Geometry written by Sławomir Dinew and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-05 with Mathematics categories.
Collecting together the lecture notes of the CIME Summer School held in Cetraro in July 2018, the aim of the book is to introduce a vast range of techniques which are useful in the investigation of complex manifolds. The school consisted of four courses, focusing on both the construction of non-Kähler manifolds and the understanding of a possible classification of complex non-Kähler manifolds. In particular, the courses by Alberto Verjovsky and Andrei Teleman introduced tools in the theory of foliations and analytic techniques for the classification of compact complex surfaces and compact Kähler manifolds, respectively. The courses by Sebastien Picard and Sławomir Dinew focused on analytic techniques in Hermitian geometry, more precisely, on special Hermitian metrics and geometric flows, and on pluripotential theory in complex non-Kähler geometry.
Locally Mixed Symmetric Spaces
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Author : Bruce Hunt
language : en
Publisher: Springer Nature
Release Date : 2021-09-04
Locally Mixed Symmetric Spaces written by Bruce Hunt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-04 with Mathematics categories.
What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common? All are related to a type of manifold called locally mixed symmetric spaces in this book. The presentation emphasizes geometric concepts and relations and gives each reader the "roter Faden", starting from the basics and proceeding towards quite advanced topics which lie at the intersection of differential and algebraic geometry, algebra and topology. Avoiding technicalities and assuming only a working knowledge of real Lie groups, the text provides a wealth of examples of symmetric spaces. The last two chapters deal with one particular case (Kuga fiber spaces) and a generalization (elliptic surfaces), both of which require some knowledge of algebraic geometry. Of interest to topologists, differential or algebraic geometers working in areas related to arithmetic groups, the book also offers an introduction to the ideas for non-experts.
Birational Geometry Of Hypersurfaces
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Author : Andreas Hochenegger
language : en
Publisher: Springer Nature
Release Date : 2019-10-08
Birational Geometry Of Hypersurfaces written by Andreas Hochenegger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-08 with Mathematics categories.
Originating from the School on Birational Geometry of Hypersurfaces, this volume focuses on the notion of (stable) rationality of projective varieties and, more specifically, hypersurfaces in projective spaces, and provides a large number of open questions, techniques and spectacular results. The aim of the school was to shed light on this vast area of research by concentrating on two main aspects: (1) Approaches focusing on (stable) rationality using deformation theory and Chow-theoretic tools like decomposition of the diagonal; (2) The connection between K3 surfaces, hyperkähler geometry and cubic fourfolds, which has both a Hodge-theoretic and a homological side. Featuring the beautiful lectures given at the school by Jean-Louis Colliot-Thélène, Daniel Huybrechts, Emanuele Macrì, and Claire Voisin, the volume also includes additional notes by János Kollár and an appendix by Andreas Hochenegger.