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Advances In Algebraic Geometry Motivated By Physics
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Book Synopsis Advances in Algebraic Geometry Motivated by Physics by : Emma Previato
Download or read book Advances in Algebraic Geometry Motivated by Physics written by Emma Previato and published by American Mathematical Soc.. This book was released on 2001 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our knowledge of objects of algebraic geometry such as moduli of curves, (real) Schubert classes, fundamental groups of complements of hyperplane arrangements, toric varieties, and variation of Hodge structures, has been enhanced recently by ideas and constructions of quantum field theory, such as mirror symmetry, Gromov-Witten invariants, quantum cohomology, and gravitational descendants. These are some of the themes of this refereed collection of papers, which grew out of the special session, ``Enumerative Geometry in Physics,'' held at the AMS meeting in Lowell, MA, April 2000. This session brought together mathematicians and physicists who reported on the latest results and open questions; all the abstracts are included as an Appendix, and also included are papers by some who could not attend. The collection provides an overview of state-of-the-art tools, links that connect classical and modern problems, and the latest knowledge available.
Book Synopsis Advances in Geometry by : Jean-Luc Brylinski
Download or read book Advances in Geometry written by Jean-Luc Brylinski and published by Birkhäuser. This book was released on 1998-12-01 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outgrowth of the activities of the Center for Geometry and Mathematical Physics (CGMP) at Penn State from 1996 to 1998. The Center was created in the Mathematics Department at Penn State in the fall of 1996 for the purpose of promoting and supporting the activities of researchers and students in and around geometry and physics at the university. The CGMP brings many visitors to Penn State and has ties with other research groups; it organizes weekly seminars as well as annual workshops The book contains 17 contributed articles on current research topics in a variety of fields: symplectic geometry, quantization, quantum groups, algebraic geometry, algebraic groups and invariant theory, and character istic classes. Most of the 20 authors have talked at Penn State about their research. Their articles present new results or discuss interesting perspec tives on recent work. All the articles have been refereed in the regular fashion of excellent scientific journals. Symplectic geometry, quantization and quantum groups is one main theme of the book. Several authors study deformation quantization. As tashkevich generalizes Karabegov's deformation quantization of Kahler manifolds to symplectic manifolds admitting two transverse polarizations, and studies the moment map in the case of semisimple coadjoint orbits. Bieliavsky constructs an explicit star-product on holonomy reducible sym metric coadjoint orbits of a simple Lie group, and he shows how to con struct a star-representation which has interesting holomorphic properties.
Book Synopsis Advances in Geometry and Lie Algebras from Supergravity by : Pietro Giuseppe Frè
Download or read book Advances in Geometry and Lie Algebras from Supergravity written by Pietro Giuseppe Frè and published by Springer. This book was released on 2018-02-24 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Enumerative Geometry and String Theory by : Sheldon Katz
Download or read book Enumerative Geometry and String Theory written by Sheldon Katz and published by American Mathematical Soc.. This book was released on 2006 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perhaps the most famous example of how ideas from modern physics have revolutionized mathematics is the way string theory has led to an overhaul of enumerative geometry, an area of mathematics that started in the eighteen hundreds. Century-old problems of enumerating geometric configurations have now been solved using new and deep mathematical techniques inspired by physics! The book begins with an insightful introduction to enumerative geometry. From there, the goal becomes explaining the more advanced elements of enumerative algebraic geometry. Along the way, there are some crash courses on intermediate topics which are essential tools for the student of modern mathematics, such as cohomology and other topics in geometry. The physics content assumes nothing beyond a first undergraduate course. The focus is on explaining the action principle in physics, the idea of string theory, and how these directly lead to questions in geometry. Once these topics are in place, the connection between physics and enumerative geometry is made with the introduction of topological quantum field theory and quantum cohomology.
Book Synopsis The Geometry of Physics by : Theodore Frankel
Download or read book The Geometry of Physics written by Theodore Frankel and published by Cambridge University Press. This book was released on 2011-11-03 with total page 749 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang–Mills, the Aharonov–Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.
Book Synopsis Orbifolds in Mathematics and Physics by : Alejandro Adem
Download or read book Orbifolds in Mathematics and Physics written by Alejandro Adem and published by American Mathematical Soc.. This book was released on 2002 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book publishes papers originally presented at a conference on the Mathematical Aspects of Orbifold String Theory, hosted by the University of Wisconsin-Madison. It contains a great deal of information not fully covered in the published literature and showcases the current state of the art in orbital string theory. The subject of orbifolds has a long prehistory, going back to the work of Thurston and Haefliger, with roots in the theory of manifolds, group actions, and foliations. The recent explosion of activity on the topic has been powered by applications of orbifolds to moduli problems and quantum field theory. The present volume presents an interdisciplinary look at orbifold problems. Topics such as stacks, vertex operator algebras, branes, groupoids, K-theory and quantum cohomology are discussed. The book reflects the thinking of distinguished investigators working in the areas of mathematical physics, algebraic geometry, algebraic topology, symplectic geometry and representation theory. By presenting the work of a broad range of mathematicians and physicists who use and study orbifolds, it familiarizes readers with the various points of view and types of results the researchers bring to the subject.
Book Synopsis Integrable Systems and Algebraic Geometry by : Ron Donagi
Download or read book Integrable Systems and Algebraic Geometry written by Ron Donagi and published by Cambridge University Press. This book was released on 2020-03-02 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.
Book Synopsis Integrable Systems and Algebraic Geometry: Volume 2 by : Ron Donagi
Download or read book Integrable Systems and Algebraic Geometry: Volume 2 written by Ron Donagi and published by Cambridge University Press. This book was released on 2020-04-02 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Created as a celebration of mathematical pioneer Emma Previato, this comprehensive second volume highlights the connections between her main fields of research, namely algebraic geometry and integrable systems. Written by leaders in the field, the text is accessible to graduate students and non-experts, as well as researchers.
Book Synopsis Quantum Symmetries in Theoretical Physics and Mathematics by : M A Lifshits
Download or read book Quantum Symmetries in Theoretical Physics and Mathematics written by M A Lifshits and published by American Mathematical Soc.. This book was released on 2002 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents articles from several lectures presented at the school on 'Quantum Symmetries in Theoretical Physics and Mathematics' held in Bariloche, Argentina. The various lecturers provided significantly different points of view on several aspects of Hopf algebras, quantum group theory, and noncommutative differential geometry, ranging from analysis, geometry, and algebra to physical models, especially in connection with integrable systems and conformal field theories. Primary topics discussed in the text include subgroups of quantum $SU(N)$, quantum ADE classifications and generalized Coxeter systems, modular invariance, defects and boundaries in conformal field theory, finite dimensional Hopf algebras, Lie bialgebras and Belavin-Drinfeld triples, real forms of quantum spaces, perturbative and non-perturbative Yang-Baxter operators, braided subfactors in operator algebras and conformal field theory, and generalized ($d^N$) cohomologies.
Author :m Summer School in Analysis and Mathematical Physics 2000 Cuernavaca Publisher :American Mathematical Soc. ISBN 13 :0821827081 Total Pages :272 pages Book Rating :4.8/5 (218 download)
Book Synopsis Second Summer School in Analysis and Mathematical Physics by : m Summer School in Analysis and Mathematical Physics 2000 Cuernavaca
Download or read book Second Summer School in Analysis and Mathematical Physics written by m Summer School in Analysis and Mathematical Physics 2000 Cuernavaca and published by American Mathematical Soc.. This book was released on 2001 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the second time, a Summer School in Analysis and Mathematical Physics took place at the Universidad Nacional Autonoma de Mexico in Cuernavaca. The purpose of the schools is to provide a bridge from standard graduate courses in mathematics to current research topics, particularly in analysis. The lectures are given by internationally recognized specialists in the fields. The topics covered in this Second Summer School include harmonic analysis, complex analysis, pseudodifferential operators, the mathematics of quantum chaos, and non-linear analysis.
Author :Ams-IMS-Siam Joint Summer Research Conference on Symbolic Computation Solving Equations I Publisher :American Mathematical Soc. ISBN 13 :0821826794 Total Pages :240 pages Book Rating :4.8/5 (218 download)
Book Synopsis Symbolic Computation by : Ams-IMS-Siam Joint Summer Research Conference on Symbolic Computation Solving Equations I
Download or read book Symbolic Computation written by Ams-IMS-Siam Joint Summer Research Conference on Symbolic Computation Solving Equations I and published by American Mathematical Soc.. This book was released on 2001 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers related to the research conference, 'Symbolic Computation: Solving Equations in Algebra, Analysis, and Engineering', held at Mount Holyoke College (MA). It provides a broad range of active research areas in symbolic computation as it applies to the solution of polynomial systems. The conference brought together pure and applied mathematicians, computer scientists, and engineers, who use symbolic computation to solve systems of equations or who develop the theoretical background and tools needed for this purpose. Within this general framework, the conference focused on several themes: systems of polynomials, systems of differential equations, non commutative systems, and applications.
Book Synopsis Advances in Wave Interaction and Turbulence by : Paul A. Milewski
Download or read book Advances in Wave Interaction and Turbulence written by Paul A. Milewski and published by American Mathematical Soc.. This book was released on 2001 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: We often think of our natural environment as being composed of very many interacting particles, undergoing individual chaotic motions, of which only very coarse averages are perceptible at scales natural to us. However, we could as well think of the world as being made out of individual waves. This is so not just because the distinction between waves and particles becomes rather blurred at the atomic level, but also because even phenomena at much larger scales are better describedin terms of waves rather than of particles: It is rare in both fluids and solids to observe energy being carried from one region of space to another by a given set of material particles; much more often, this transfer occurs through chains of particles, neither of them moving much, but eachcommunicating with the next, and hence creating these immaterial objects we call waves. Waves occur at many spatial and temporal scales. Many of these waves have small enough amplitude that they can be approximately described by linear theory. However, the joint effect of large sets of waves is governed by nonlinear interactions which are responsible for huge cascades of energy among very disparate scales. Understanding these energy transfers is crucial in order to determine the response oflarge systems, such as the atmosphere and the ocean, to external forcings and dissipation mechanisms which act on scales decades apart. The field of wave turbulence attempts to understand the average behavior of large ensembles of waves, subjected to forcing and dissipation at opposite ends of theirspectrum. It does so by studying individual mechanisms for energy transfer, such as resonant triads and quartets, and attempting to draw from them effects that should not survive averaging. This book presents the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Dispersive Wave Turbulence held at Mt. Holyoke College (MA). It drew together a group of researchers from many corners of the world, in the context of a perceived renaissance of the field, driven by heated debate aboutthe fundamental mechanism of energy transfer among large sets of waves, as well as by novel applications-and old ones revisited-to the understanding of the natural world. These proceedings reflect the spirit that permeated the conference, that of friendly scientific disagreement and genuine wonderat the rich phenomenology of waves.
Book Synopsis Recent Advances in Numerical Methods for Partial Differential Equations and Applications by : Xiaobing Feng
Download or read book Recent Advances in Numerical Methods for Partial Differential Equations and Applications written by Xiaobing Feng and published by American Mathematical Soc.. This book was released on 2002 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: An emerging field over the past 15 years, computational mathematics is a vast area which has experienced major developments in both algorithmic advances and applications to other fields. These developments have had profound implications in mathematics, science, engineering and industry. Compiled here are six of nine in-depth survey papers with an expository discussion on computational mathematics that were presented at the 2001 John H. Barrett Memorial Lectures at the University of Tennessee, Knoxville. They focus on parallel numerical algorithms for partial differential equations, their implementation and applications in fluid mechanics and material science. Each of the lecturers is a leading researcher in the field of computational mathematics and its applications. This book will be a useful reference for graduate students as well as the many groups of researchers working in advanced computations, including engineering and computer scientists. Prior knowledge of partial differential equations and their numerical methods is helpful.
Author :Geometry AMS-IMS-SIAM Joint Summer Research Conference on Groupoids in Analysis Publisher :American Mathematical Soc. ISBN 13 :0821820427 Total Pages :192 pages Book Rating :4.8/5 (218 download)
Book Synopsis Groupoids in Analysis, Geometry, and Physics by : Geometry AMS-IMS-SIAM Joint Summer Research Conference on Groupoids in Analysis
Download or read book Groupoids in Analysis, Geometry, and Physics written by Geometry AMS-IMS-SIAM Joint Summer Research Conference on Groupoids in Analysis and published by American Mathematical Soc.. This book was released on 2001 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groupoids often occur when there is symmetry of a nature not expressible in terms of groups. Other uses of groupoids can involve something of a dynamical nature. Indeed, some of the main examples come from group actions. It should also be noted that in many situations where groupoids have been used, the main emphasis has not been on symmetry or dynamics issues. For example, a foliation is an equivalence relation and has another groupoid associated with it, called the holonomy groupoid. While the implicit symmetry and dynamics are relevant, the groupoid records mostly the structure of the space of leaves and the holonomy.More generally, the use of groupoids is very much related to various notions of orbit equivalence. The point of view that groupoids describe 'singular spaces' can be found in the work of A. Grothendieck and is prevalent in the non-commutative geometry of A. Connes. This book presents the proceedings from the Joint Summer Research Conference on 'Groupoids in Analysis, Geometry, and Physics' held in Boulder, CO. The book begins with an introduction to ways in which groupoids allow a more comprehensive view of symmetry than is seen via groups. Topics range from foliations, pseudo-differential operators, $KK$-theory, amenability, Fell bundles, and index theory to quantization of Poisson manifolds. Readers will find examples of important tools for working with groupoids. This book is geared to students and researchers. It is intended to improve their understanding of groupoids and to encourage them to look further while learning about the tools used.
Book Synopsis Recent Progress in Homotopy Theory by : Donald M. Davis
Download or read book Recent Progress in Homotopy Theory written by Donald M. Davis and published by American Mathematical Soc.. This book was released on 2002 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings from the month-long program held at Johns Hopkins University (Baltimore, MD) on homotopy theory, sponsored by the Japan-U.S. Mathematics Institute (JAMI). The book begins with historical accounts on the work of Professors Peter Landweber and Stewart Priddy. Central among the other topics are the following: 1. classical and nonclassical theory of $H$-spaces, compact groups, and finite groups, 2. classical and chromatic homotopy theory andlocalization, 3. classical and topological Hochschild cohomology, 4. elliptic cohomology and its relation to Moonshine and topological modular forms, and 5. motivic cohomology and Chow rings. This volume surveys the current state of research in these areas and offers an overview of futuredirections.
Book Synopsis $q$-Series with Applications to Combinatorics, Number Theory, and Physics by : Bruce C. Berndt
Download or read book $q$-Series with Applications to Combinatorics, Number Theory, and Physics written by Bruce C. Berndt and published by American Mathematical Soc.. This book was released on 2001 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of $q$-series can be said to begin with Euler and his pentagonal number theorem. In fact, $q$-series are sometimes called Eulerian series. Contributions were made by Gauss, Jacobi, and Cauchy, but the first attempt at a systematic development, especially from the point of view of studying series with the products in the summands, was made by E. Heine in 1847. In the latter part of the nineteenth and in the early part of the twentieth centuries, two Englishmathematicians, L. J. Rogers and F. H. Jackson, made fundamental contributions. In 1940, G. H. Hardy described what we now call Ramanujan's famous $ 1\psi 1$ summation theorem as ``a remarkable formula with many parameters.'' This is now one of the fundamental theorems of the subject. Despite humble beginnings,the subject of $q$-series has flourished in the past three decades, particularly with its applications to combinatorics, number theory, and physics. During the year 2000, the University of Illinois embraced The Millennial Year in Number Theory. One of the events that year was the conference $q$-Series with Applications to Combinatorics, Number Theory, and Physics. This event gathered mathematicians from the world over to lecture and discuss their research. This volume presents nineteen of thepapers presented at the conference. The excellent lectures that are included chart pathways into the future and survey the numerous applications of $q$-series to combinatorics, number theory, and physics.
Book Synopsis Integrable Systems, Topology, and Physics by : Martin A. Guest
Download or read book Integrable Systems, Topology, and Physics written by Martin A. Guest and published by American Mathematical Soc.. This book was released on 2002 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideas and techniques from the theory of integrable systems are playing an increasingly important role in geometry. Thanks to the development of tools from Lie theory, algebraic geometry, symplectic geometry, and topology, classical problems are investigated more systematically. New problems are also arising in mathematical physics. A major international conference was held at the University of Tokyo in July 2000. It brought together scientists in all of the areas influenced by integrable systems. This book is the second of three collections of expository and research articles. This volume focuses on topology and physics. The role of zero curvature equations outside of the traditional context of differential geometry has been recognized relatively recently, but it has been an extraordinarily productive one, and most of the articles in this volume make some reference to it. Symplectic geometry, Floer homology, twistor theory, quantum cohomology, and the structure of special equations of mathematical physics, such as the Toda field equations--all of these areas have gained from the integrable systems point of view and contributed to it. Many of the articles in this volume are written by prominent researchers and will serve as introductions to the topics. It is intended for graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics. The first volume from this conference also available from the AMS is Differential Geometry and Integrable Systems, Volume 308 CONM/308 in the Contemporary Mathematics series. The forthcoming third volume will be published by the Mathematical Society of Japan and will be available outside of Japan from the AMS in the Advanced Studies in Pure Mathematics series.
