Higher Structures In Topology Geometry And Physics
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Higher Structures In Topology Geometry And Physics
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Author : Ralph M. Kaufmann
language : en
Publisher: American Mathematical Society
Release Date : 2024-07-03
Higher Structures In Topology Geometry And Physics written by Ralph M. Kaufmann 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 2024-07-03 with Mathematics categories.
This volume contains the proceedings of the AMS Special Session on Higher Structures in Topology, Geometry, and Physics, held virtually on March 26–27, 2022. The articles give a snapshot survey of the current topics surrounding the mathematical formulation of field theories. There is an intricate interplay between geometry, topology, and algebra which captures these theories. The hallmark are higher structures, which one can consider as the secondary algebraic or geometric background on which the theories are formulated. The higher structures considered in the volume are generalizations of operads, models for conformal field theories, string topology, open/closed field theories, BF/BV formalism, actions on Hochschild complexes and related complexes, and their geometric and topological aspects.
Higher Structures In Geometry And Physics
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Author : Alberto S. Cattaneo
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-25
Higher Structures In Geometry And Physics written by Alberto S. Cattaneo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-25 with Mathematics categories.
This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics— such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. The volume is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures.
New Foundations For Physical Geometry
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Author : Tim Maudlin
language : en
Publisher:
Release Date : 2014-02
New Foundations For Physical Geometry written by Tim Maudlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02 with Mathematics categories.
Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
Riemann Topology And Physics
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Author : Michael I. Monastyrsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-08
Riemann Topology And Physics written by Michael I. Monastyrsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-08 with Mathematics categories.
Ten years have passed since the publication of the first English edition. "Ten years is a long time, even when you are not in jail. " If we recall that the article on Riemann appeared in (Nature) in 1976, this Russian vaudeville joke is more than - propriate. Only the author's youth can account for the insane enterprise of presenting the scientific achievements and the biography of Riemann in 60 pages and the c- nection between physics and topology in the same space. Judging from the fact that the book sold out and got favorable reviews, there is a demand for publications of this type. It seems to me that popularizations aimed not at a narrow specialist but at a broader reader are especially needed nowadays. Specialists obtain information in their fields almost instantly thanks to the Internet, but to find out what is happening in contiguous fields, what problems and results are of great interest here, is not at all easy. Returning to my own book, I note with a certain pride that at least I seem to have evaluated accurately the trends in the development of theoretical physics. It is the combination of physics with topology and algebraic geometry that has led to the brightest achievements of mathematical physics in the last decade. It suffices to note the remarkable results of S.
Topology And Physics
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Author : Chen Ning Yang
language : en
Publisher: World Scientific Publishing Company
Release Date : 2019-03-11
Topology And Physics written by Chen Ning Yang and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-11 with Science categories.
Since its birth in Poincaré's seminal 1894 'Analysis Situs', topology has become a cornerstone of mathematics. As with all beautiful mathematical concepts, topology inevitably -- resonating with that Wignerian principle of the effectiveness of mathematics in the natural sciences -- finds its prominent role in physics. From Chern-Simons theory to topological quantum field theory, from knot invariants to Calabi-Yau compactification in string theory, from spacetime topology in cosmology to the recent Nobel Prize winning work on topological insulators, the interactions between topology and physics have been a triumph over the past few decades.In this eponymous volume, we are honoured to have contributions from an assembly of grand masters of the field, guiding us with their world-renowned expertise on the subject of the interplay between 'Topology' and 'Physics'. Beginning with a preface by Chen Ning Yang on his recollections of the early days, we proceed to a novel view of nuclei from the perspective of complex geometry by Sir Michael Atiyah and Nick Manton, followed by an entrée toward recent developments in two-dimensional gravity and intersection theory on the moduli space of Riemann surfaces by Robbert Dijkgraaf and Edward Witten; a study of Majorana fermions and relations to the Braid group by Louis H Kauffman; a pioneering investigation on arithmetic gauge theory by Minhyong Kim; an anecdote-enriched review of singularity theorems in black-hole physics by Sir Roger Penrose; an adventure beyond anyons by Zhenghan Wang; an aperçu on topological insulators from first-principle calculations by Haijun Zhang and Shou-Cheng Zhang; finishing with synopsis on quantum information theory as one of the four revolutions in physics and the second quantum revolution by Xiao-Gang Wen. We hope that this book will serve to inspire the research community.
Higher Structures In Geometry And Physics
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Author : Alberto S. Cattaneo
language : en
Publisher: Birkhäuser
Release Date : 2010-12-03
Higher Structures In Geometry And Physics written by Alberto S. Cattaneo and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-03 with Mathematics categories.
This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics— such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. The volume is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures.
Topology Geometry And Gauge Fields
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Author : Gregory L. Naber
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Topology Geometry And Gauge Fields written by Gregory L. Naber and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development ofnewcourses is a natural consequence of a high levelof excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied mathe matical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface In Egypt, geometry was created to measure the land. Similar motivations, on a somewhat larger scale, led Gauss to the intrinsic differential geometry of surfaces in space. Newton created the calculus to study the motion of physical objects (apples, planets, etc.) and Poincare was similarly impelled toward his deep and far-reaching topological view of dynamical systems.
Differential Topology And Geometry With Applications To Physics
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Author : Eduardo Nahmad-Achar
language : en
Publisher:
Release Date : 2018
Differential Topology And Geometry With Applications To Physics written by Eduardo Nahmad-Achar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Geometry, Differential categories.
"Differential geometry has encountered numerous applications in physics. More and more physical concepts can be understood as a direct consequence of geometric principles. The mathematical structure of Maxwell's electrodynamics, of the general theory of relativity, of string theory, and of gauge theories, to name but a few, are of a geometric nature. All of these disciplines require a curved space for the description of a system, and we require a mathematical formalism that can handle the dynamics in such spaces if we wish to go beyond a simple and superficial discussion of physical relationships. This formalism is precisely differential geometry. Even areas like thermodynamics and fluid mechanics greatly benefit from a differential geometric treatment. Not only in physics, but in important branches of mathematics has differential geometry effected important changes. Aimed at graduate students and requiring only linear algebra and differential and integral calculus, this book presents, in a concise and direct manner, the appropriate mathematical formalism and fundamentals of differential topology and differential geometry together with essential applications in many branches of physics." -- Prové de l'editor.
Higher Operads Higher Categories
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Author : Tom Leinster
language : en
Publisher: Cambridge University Press
Release Date : 2004-07-22
Higher Operads Higher Categories written by Tom Leinster 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 2004-07-22 with Mathematics categories.
Foundations of higher dimensional category theory for graduate students and researchers in mathematics and mathematical physics.
From Representation Theory To Mathematical Physics And Back
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Author : Mikhail Khovanov
language : en
Publisher: American Mathematical Society
Release Date : 2025-05-14
From Representation Theory To Mathematical Physics And Back written by Mikhail Khovanov 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 2025-05-14 with Mathematics categories.
This volume is a proceedings of a workshop at the Simons Center for Geometry and Physics from May 31– June 4, 2022. The workshop highlighted progress in the areas of vertex operator algebras, conformal field theory, categorification, low dimensional topology and representation theory of affine Lie algebras, loop groups, and quantum groups. In the past 40 years, string theory gave rise to the mathematical theory of vertex operator algebras, which led to the construction of representations of affine Lie algebras and the Moonshine module of the Monster group. These mathematical constructions have in turn led to ideas about 3-dimensional quantum gravity. In another direction, the discovery of the Jones polynomial led to a physical construction of 3-dimensional topological quantum field theories (TQFTs), which in turn advanced many mathematical developments in quantum groups and low dimensional topology. Louis Crane and Igor Frenkel introduced the categorification program with the goal of upgrading 3-dimensional TQFTs coming from representation theory of quantum groups to 4-dimensional TQFTs. This idea gave rise to the development of link homologies constructed from representation-theoretic, algebraic-geometric, combinatorial, and physical structures. Articles in this volume present both classical and new results related to these topics. They will be interesting to researchers and graduate students working in mathematical aspects of modern quantum field theory.