Download or read book Chern Simons Theory Matrix Models and Topological Strings written by Marcos Marino and published by Oxford University Press. This book was released on 2005-09-22 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the old idea that gauge theories and string theories are equivalent has been implemented and developed in various ways, and there are by now various models where the string theory / gauge theory correspondence is at work. One of the most important examples of this correspondence relates Chern-Simons theory, a topological gauge theory in three dimensions which describes knot and three-manifold invariants, to topological string theory, which is deeply related to Gromov-Witten invariants. This has led to some surprising relations between three-manifold geometry and enumerative geometry. This book gives the first coherent presentation of this and other related topics. After an introduction to matrix models and Chern-Simons theory, the book describes in detail the topological string theories that correspond to these gauge theories and develops the mathematical implications of this duality for the enumerative geometry of Calabi-Yau manifolds and knot theory. It is written in a pedagogical style and will be useful reading for graduate students and researchers in both mathematics and physics willing to learn about these developments.
Download or read book Chern Simons Theory Matrix Models and Topological Strings written by Marcos Marino and published by Oxford University Press. This book was released on 2005 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to some of the most recent developments in string theory, and in particular to their mathematical implications and their impact in knot theory and algebraic geometry.
Download or read book Chern Simons Theory Matrix Models and Topological Strings written by Marcos Marino and published by . This book was released on 2005 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topological Strings and Quantum Curves written by Lotte Hollands and published by Amsterdam University Press. This book was released on 2009 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents several new insights on the interface between mathematics and theoretical physics, with a central role for Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW models is embedded in string theory. Secondly, this model is generalized to a web of dualities connecting topological string theory and N=2 supersymmetric gauge theories to a configuration of D-branes that intersect over a Riemann surface. This description yields a new perspective on topological string theory in terms of a KP integrable system based on a quantum curve. Thirdly, this thesis describes a geometric analysis of wall-crossing in N=4 string theory. And lastly, it offers a novel approach to constuct metastable vacua in type IIB string theory.
Download or read book Advanced Topics in Quantum Mechanics written by Marcos Mariño and published by Cambridge University Press. This book was released on 2021-12-09 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics is one of the most successful theories in science, and is relevant to nearly all modern topics of scientific research. This textbook moves beyond the introductory and intermediate principles of quantum mechanics frequently covered in undergraduate and graduate courses, presenting in-depth coverage of many more exciting and advanced topics. The author provides a clearly structured text for advanced students, graduates and researchers looking to deepen their knowledge of theoretical quantum mechanics. The book opens with a brief introduction covering key concepts and mathematical tools, followed by a detailed description of the Wentzel–Kramers–Brillouin (WKB) method. Two alternative formulations of quantum mechanics are then presented: Wigner's phase space formulation and Feynman's path integral formulation. The text concludes with a chapter examining metastable states and resonances. Step-by-step derivations, worked examples and physical applications are included throughout.
Download or read book Homological Mirror Symmetry written by Anton Kapustin and published by Springer Science & Business Media. This book was released on 2009 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: An ideal reference on the mathematical aspects of quantum field theory, this volume provides a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives.
Download or read book Geometry of String Theory Compactifications written by Alessandro Tomasiello and published by Cambridge University Press. This book was released on 2022-01-13 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified perspective on new and advanced mathematical techniques used in string theory research for graduate students and researchers.
Download or read book Applications of Random Matrices in Physics written by Édouard Brezin and published by Springer Science & Business Media. This book was released on 2006-07-03 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical physicist. Mathematical methods inspired by random matrix theory become more powerful, sophisticated and enjoy rapidly growing applications in physics. Recent examples include the calculation of universal correlations in the mesoscopic system, new applications in disordered and quantum chaotic systems, in combinatorial and growth models, as well as the recent breakthrough, due to the matrix models, in two dimensional gravity and string theory and the non-abelian gauge theories. The book consists of the lectures of the leading specialists and covers rather systematically many of these topics. It can be useful to the specialists in various subjects using random matrices, from PhD students to confirmed scientists.
Download or read book Stacks and Categories in Geometry Topology and Algebra written by Tony Pantev and published by American Mathematical Soc.. This book was released on 2015-06-26 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the CATS4 Conference on Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, held from July 2-7, 2012, at CIRM in Luminy, France. Over the past several years, the CATS conference series has brought together top level researchers from around the world interested in relative and higher category theory and its applications to classical mathematical domains. Included in this volume is a collection of articles covering the applications of categories and stacks to geometry, topology and algebra. Techniques such as localization, model categories, simplicial objects, sheaves of categories, mapping stacks, dg structures, hereditary categories, and derived stacks, are applied to give new insight on cluster algebra, Lagrangians, trace theories, loop spaces, structured surfaces, stability, ind-coherent complexes and 1-affineness showing up in geometric Langlands, branching out to many related topics along the way.
Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer Nature. This book was released on 2021-07-14 with total page 929 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021. The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics.
Download or read book Modular Forms and String Duality written by Noriko Yui, Helena Verrill, and Charles F. Doran and published by American Mathematical Soc.. This book was released on with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is a testimony to the BIRS Workshop, and it covers a wide range of topics at the interface of number theory and string theory, with special emphasis on modular forms and string duality. They include the recent advances as well as introductory expositions on various aspects of modular forms, motives, differential equations, conformal field theory, topological strings and Gromov-Witten invariants, mirror symmetry, and homological mirror symmetry. The contributions are roughly divided into three categories: arithmetic and modular forms, geometric and differential equations, and physics and string theory. The book is suitable for researchers working at the interface of number theory and string theory."--BOOK JACKET.
Download or read book Applications of Random Matrices in Physics written by Édouard Brezin and published by Springer Science & Business Media. This book was released on 2006-03-03 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute on Applications of Random Matrices in Physics, Les Houches, France, 6-25 June 2004
Download or read book String Math 2011 written by Jonathan Block and published by American Mathematical Soc.. This book was released on 2012 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nature of interactions between mathematicians and physicists has been thoroughly transformed in recent years. String theory and quantum field theory have contributed a series of profound ideas that gave rise to entirely new mathematical fields and revitalized older ones. The influence flows in both directions, with mathematical techniques and ideas contributing crucially to major advances in string theory. A large and rapidly growing number of both mathematicians and physicists are working at the string-theoretic interface between the two academic fields. The String-Math conference series aims to bring together leading mathematicians and mathematically minded physicists working in this interface. This volume contains the proceedings of the inaugural conference in this series, String-Math 2011, which was held June 6-11, 2011, at the University of Pennsylvania.
Download or read book Geometry and Statistics written by and published by Academic Press. This book was released on 2022-07-15 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry and Statistics, Volume 46 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. - Provides the authority and expertise of leading contributors from an international board of authors - Presents the latest release in the Handbook of Statistics series - Updated release includes the latest information on Geometry and Statistics
Download or read book Homological Mirror Symmetry and Tropical Geometry written by Ricardo Castano-Bernard and published by Springer. This book was released on 2014-10-07 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Topological Quantum Field Theory and Four Manifolds written by Jose Labastida and published by Springer Science & Business Media. This book was released on 2007-07-18 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergence of topological quantum ?eld theory has been one of the most important breakthroughs which have occurred in the context of ma- ematical physics in the last century, a century characterizedbyindependent developments of the main ideas in both disciplines, physics and mathematics, which has concluded with two decades of strong interaction between them, where physics, as in previous centuries, has acted as a source of new mat- matics. Topological quantum ?eld theories constitute the core of these p- nomena, although the main drivingforce behind it has been the enormous e?ort made in theoretical particle physics to understand string theory as a theory able to unify the four fundamental interactions observed in nature. These theories set up a new realm where both disciplines pro?t from each other. Although the most striking results have appeared on the mathema- calside,theoreticalphysicshasclearlyalsobene?tted,sincethecorresponding developments have helped better to understand aspects of the fundamentals of ?eld and string theory.
Download or read book Mirror Symmetry and Algebraic Geometry written by David A. Cox and published by American Mathematical Soc.. This book was released on 1999 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in four-dimensional projective space. Understanding the mathematics behind these predictions has been a substantial challenge. This book is the first completely comprehensive monograph on mirror symmetry, covering the original observations by the physicists through the most recent progress made to date. Subjects discussed include toric varieties, Hodge theory, Kahler geometry, moduli of stable maps, Calabi-Yau manifolds, quantum cohomology, Gromov-Witten invariants, and the mirror theorem. This title features: numerous examples worked out in detail; an appendix on mathematical physics; an exposition of the algebraic theory of Gromov-Witten invariants and quantum cohomology; and, a proof of the mirror theorem for the quintic threefold.
