Advances In Algebraic Geometry Motivated By Physics

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Advances in Algebraic Geometry Motivated by Physics

Emma Previato
Advances in Algebraic Geometry Motivated by Physics Book PDF

Author : Emma Previato
Publisher : American Mathematical Soc.
Page : 310 pages
File Size : 41,7 Mb
Release : 2001
Category : Geometry, Algebraic
ISBN : 9780821828106

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Advances in Algebraic Geometry Motivated by Physics by Emma Previato Pdf

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.

Advances in Geometry

Jean-Luc Brylinski,Ranee Brylinski,Victor Nistor
Advances in Geometry Book PDF

Author : Jean-Luc Brylinski,Ranee Brylinski,Victor Nistor
Publisher : Birkhäuser
Page : 403 pages
File Size : 42,8 Mb
Release : 1998-12-01
Category : Mathematics
ISBN : 0817640444

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Advances in Geometry by Jean-Luc Brylinski,Ranee Brylinski,Victor Nistor Pdf

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.

Higher Structures in Geometry and Physics

Alberto S. Cattaneo,Anthony Giaquinto,Ping Xu
Higher Structures in Geometry and Physics Book PDF

Author : Alberto S. Cattaneo,Anthony Giaquinto,Ping Xu
Publisher : Birkhäuser
Page : 362 pages
File Size : 53,7 Mb
Release : 2010-12-03
Category : Mathematics
ISBN : 0817647341

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Higher Structures in Geometry and Physics by Alberto S. Cattaneo,Anthony Giaquinto,Ping Xu Pdf

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.

Enumerative Geometry and String Theory

Sheldon Katz
Enumerative Geometry and String Theory Book PDF

Author : Sheldon Katz
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 54,6 Mb
Release : 2006
Category : Geometry, Enumerative
ISBN : 9780821836873

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Enumerative Geometry and String Theory by Sheldon Katz Pdf

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.

Integrable Systems and Algebraic Geometry

Ron Donagi,Tony Shaska
Integrable Systems and Algebraic Geometry Book PDF

Author : Ron Donagi,Tony Shaska
Publisher : Cambridge University Press
Page : 421 pages
File Size : 54,9 Mb
Release : 2020-04-02
Category : Mathematics
ISBN : 9781108715744

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Integrable Systems and Algebraic Geometry by Ron Donagi,Tony Shaska Pdf

A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Advances in Geometry and Lie Algebras from Supergravity

Pietro Giuseppe Frè
Advances in Geometry and Lie Algebras from Supergravity Book PDF

Author : Pietro Giuseppe Frè
Publisher : Springer
Page : 556 pages
File Size : 51,8 Mb
Release : 2018-02-24
Category : Science
ISBN : 9783319744919

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Advances in Geometry and Lie Algebras from Supergravity by Pietro Giuseppe Frè Pdf

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.

Integrable Systems and Algebraic Geometry

Ron Donagi,Tony Shaska
Integrable Systems and Algebraic Geometry Book PDF

Author : Ron Donagi,Tony Shaska
Publisher : Cambridge University Press
Page : 537 pages
File Size : 52,5 Mb
Release : 2020-03-02
Category : Mathematics
ISBN : 9781108715775

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Integrable Systems and Algebraic Geometry by Ron Donagi,Tony Shaska Pdf

A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Symbolic Computation

Ams-IMS-Siam Joint Summer Research Conference on Symbolic Computation Solving Equations I,Ams-Ims-Siam Joint Summer Research Conference on Symbolic Computation
Symbolic Computation Book PDF

Author : Ams-IMS-Siam Joint Summer Research Conference on Symbolic Computation Solving Equations I,Ams-Ims-Siam Joint Summer Research Conference on Symbolic Computation
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 50,6 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821826799

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Symbolic Computation by Ams-IMS-Siam Joint Summer Research Conference on Symbolic Computation Solving Equations I,Ams-Ims-Siam Joint Summer Research Conference on Symbolic Computation Pdf

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.

Second Summer School in Analysis and Mathematical Physics

m Summer School in Analysis and Mathematical Physics 2000 Cuernavaca,Salvador Pérez-Esteva,Carlos Villegas-Blas,Summer School in Analysis and Mathematical Physics
Second Summer School in Analysis and Mathematical Physics Book PDF

Author : m Summer School in Analysis and Mathematical Physics 2000 Cuernavaca,Salvador Pérez-Esteva,Carlos Villegas-Blas,Summer School in Analysis and Mathematical Physics
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 43,5 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821827086

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Second Summer School in Analysis and Mathematical Physics by m Summer School in Analysis and Mathematical Physics 2000 Cuernavaca,Salvador Pérez-Esteva,Carlos Villegas-Blas,Summer School in Analysis and Mathematical Physics Pdf

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.

Groupoids in Analysis, Geometry, and Physics

Geometry AMS-IMS-SIAM Joint Summer Research Conference on Groupoids in Analysis,Arlan Ramsay,Jean Renault,AMS-IMS-SIAM JOINT SUMMER RESEARCH CONFERENCE ON G,Geometry Ams-Ims-Siam Joint Summer Research Conference on Groupoids I
Groupoids in Analysis Geometry and Physics Book PDF

Author : Geometry AMS-IMS-SIAM Joint Summer Research Conference on Groupoids in Analysis,Arlan Ramsay,Jean Renault,AMS-IMS-SIAM JOINT SUMMER RESEARCH CONFERENCE ON G,Geometry Ams-Ims-Siam Joint Summer Research Conference on Groupoids I
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 42,7 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821820421

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Groupoids in Analysis, Geometry, and Physics by Geometry AMS-IMS-SIAM Joint Summer Research Conference on Groupoids in Analysis,Arlan Ramsay,Jean Renault,AMS-IMS-SIAM JOINT SUMMER RESEARCH CONFERENCE ON G,Geometry Ams-Ims-Siam Joint Summer Research Conference on Groupoids I Pdf

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.

Advances in Wave Interaction and Turbulence

Paul A. Milewski,Laslie M. Smith,Fabian Waleffe,Esteban G. Tabak
Advances in Wave Interaction and Turbulence Book PDF

Author : Paul A. Milewski,Laslie M. Smith,Fabian Waleffe,Esteban G. Tabak
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 48,6 Mb
Release : 2001
Category : Turbulence
ISBN : 9780821827147

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Advances in Wave Interaction and Turbulence by Paul A. Milewski,Laslie M. Smith,Fabian Waleffe,Esteban G. Tabak Pdf

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.

Recent Advances in Numerical Methods for Partial Differential Equations and Applications

Xiaobing Feng,Tim P. Schulze
Recent Advances in Numerical Methods for Partial Differential Equations and Applications Book PDF

Author : Xiaobing Feng,Tim P. Schulze
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 41,8 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821829707

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Recent Advances in Numerical Methods for Partial Differential Equations and Applications by Xiaobing Feng,Tim P. Schulze Pdf

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.

Orbifolds in Mathematics and Physics

Alejandro Adem,Jack Morava,Yongbin Ruan
Orbifolds in Mathematics and Physics Book PDF

Author : Alejandro Adem,Jack Morava,Yongbin Ruan
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 49,7 Mb
Release : 2002
Category : Mathematical physics
ISBN : 9780821829905

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Orbifolds in Mathematics and Physics by Alejandro Adem,Jack Morava,Yongbin Ruan Pdf

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.

$q$-Series with Applications to Combinatorics, Number Theory, and Physics

Bruce C. Berndt,Ken Ono
q Series with Applications to Combinatorics Number Theory and Physics Book PDF

Author : Bruce C. Berndt,Ken Ono
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 42,7 Mb
Release : 2001
Category : q-series
ISBN : 9780821827468

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$q$-Series with Applications to Combinatorics, Number Theory, and Physics by Bruce C. Berndt,Ken Ono Pdf

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.

Algebraic Number Theory and Algebraic Geometry

S. V. Vostokov,Yuri Zarhin
Algebraic Number Theory and Algebraic Geometry Book PDF

Author : S. V. Vostokov,Yuri Zarhin
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 55,7 Mb
Release : 2002
Category : Algebraic number theory
ISBN : 9780821832677

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Algebraic Number Theory and Algebraic Geometry by S. V. Vostokov,Yuri Zarhin Pdf

A. N. Parshin is a world-renowned mathematician who has made significant contributions to number theory through the use of algebraic geometry. Articles in this volume present new research and the latest developments in algebraic number theory and algebraic geometry and are dedicated to Parshin's sixtieth birthday. Well-known mathematicians contributed to this volume, including, among others, F. Bogomolov, C. Deninger, and G. Faltings. The book is intended for graduate students andresearch mathematicians interested in number theory, algebra, and algebraic geometry.