This volume contains intense studies on Quantum Groups, Knot Theory, Statistical Mechanics, Conformal Field Theory, Differential Geometry and Differential Equation Methods and so on. It has contributions by renowned experts and covers most of the recent developments in these fields.
This proceedings reports on some of the most recent advances on the interaction between Differential Geometry and Theoretical Physics, a very active and exciting area of contemporary research.The papers are grouped into the following four broad categories: Geometric Methods, Noncommutative Geometry, Quantum Gravity and Topological Quantum Field Theory. A few of the topics covered are Chern-Simons Theory and Generalizations, Knot Invariants, Models of 2D Gravity, Quantum Groups and Strings on Black Holes.
C N Yang, one of the greatest physicists of the 20th Century, was awarded the Nobel Prize in 1957, jointly with T D Lee, for their investigation of the relationship (parity symmetry) between left- and right-handed states, leading to a discovery that astounded the world of physics ? the nonconservation of parity by elementary particles and their reactions. With R L Mills, he created the concept of non-abelian gauge theories, the foundation of the modern description of elementary particles and forces. Professor Yang has worked on a wide range of subjects in physics, but his abiding interests have been symmetry principles, particle physics, and statistical mechanics.In 1999, a symposium was held at the State University of New York at Stony Brook to mark the retirement of C N Yang as Einstein Professor and Director of the Institute for Theoretical Physics, and to celebrate his many achievements. A noteworthy selection of the papers presented at the symposium appears in this invaluable volume in honor of Professor Yang.
Contents:Millennium Lecture — Cairo, 15 January 2000 (M Atiyah)Trends for Science and Mathematics in the 21st Century (P A Griffiths)Arabic Mathematics and Rewriting the History of Mathematics (R Rashed)The Paradigm Shift in Mathematics Education: A Scenario for Change (W Ebeid)Einstein's Theory of Spacetime and Gravity (J Ehlers)Moduli Problems in Geometry (M S Narasimhan)Enumerative Geometry from the Greeks to Strings (C Procesi)Optical Solitons: Twenty-Seven Years of the Last Millennium and Three More Years of the New? (R K Bullough)Concepts of Non-Smooth Dynamical Systems (T Küpper)Radical Theory: Developments and Trends (R Wiegandt)On Minimal Subgroups of Finite Groups (M Asaad)Totally and Mutually Permutable Products of Finite Groups (A Ballester-Bolinches)Asymptotic Behaviour of Solutions of Evolution Equations (B Basit)On Nonlinear Evolution Equations with Applications (L Debnath)A Robust Layer-Resolving Numerical Method for a Free Convection Problem (J Étienne et al.)Growth Value-Distribution and Zero-Free Regions of Entire Functions and Sections (F F Abi-Khuzam)Three Linear Preserver Problems (A R Sourour)Prediction: Advances and New Research (E K Al-Hussaini)Inference on Parameters of the Laplace Distribution Based on Type-II Censored Samples Using Edgeworth Approximation (N Balakrishnan et al.)Mathematical Models in the Theory of Accelerated Experiments (V Bagdonavicius & M Nikulin)The Vibrations of a Drum with Fractal Boundary (J Fleckinger-Pellé)Intermediate States: Some Nonclassical Properties (M S Abdalla & A-S F Obada)On the Relativistic Two-Body Equation (S R Komy)Singularities in General Relativity and the Origin of Charge (K Buchner)The Inner Geometry of Light Cone in Godel Universe (M Abdel-Megied) Readership: Mathematicians. Keywords:Proceedings;Conference;Mathematics;Cairo (Egypt)
This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields. The contributions promise to play an important role in promoting the developments in these exciting areas. Besides the plenary talks, the coverage includes: models and related topics in statistical physics; quantum fields, strings and M-theory; Yang-Mills fields, knot theory and related topics; K-theory, including index theory and non-commutative geometry; mirror symmetry, conformal and topological quantum field theory; development of integrable systems; and random matrix theory.
This volume gives a representative survey of recent developments in relativistic and non-relativistic quantum theory, which are related to the application of symmetries in their most general sense. The corresponding mathematical notions are centered upon groups, algebras and their generalizations, and are applied in interaction with topology, differential geometry, functional analysis and related fields. Special emphasis is on results in the following areas: quantization methods, nonlinear evolution equations, foundation of quantum physics, algebraic quantum field theory, gauge and string theories, quantum information, quantum groups, discrete symmetries.
This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields. The contributions promise to play an important role in promoting the developments in these exciting areas. Besides the plenary talks, the coverage includes: models and related topics in statistical physics; quantum fields, strings and M-theory; Yang-Mills fields, knot theory and related topics; K-theory, including index theory and non-commutative geometry; mirror symmetry, conformal and topological quantum field theory; development of integrable systems; and random matrix theory. Sample Chapter(s). Chapter 1: Yangian and Applications (787 KB). Contents: Yangian and Applications (C-M Bai et al.); The Hypoelliptic Laplacian and the ChernOCoGaussOCoBonnet (J-M Bismut); S S Chern and ChernOCoSimos Terms (R Jackiw); Localization and Conjectures from String Duality (K F Liu); Topologization of Electron Liquids with ChernOCoSimons Theory and Quantum Computation (Z H Wang); Topology and Quantum Information (L H Kauffman); Toeplitz Quantization and Symplectic Reduction (X N Ma & W P Zhang); Murphy Operators in Knot Theory (H R Morton); Separation Between Spin and Charge in SU(2) YangOCoMills Theory (A J Niemi); LAwner Equations and Dispersionless Hierarchies (K Takasaki & T Takebe); and other papers. Readership: Graduate students and professional researchers in geometry and physics."
The Stony Brook Conference, "Graphs and Patterns in Mathematics and Theoretical Physics", was dedicated to Dennis Sullivan in honor of his sixtieth birthday. The event's scientific content, which was suggested by Sullivan, was largely based on mini-courses and survey lectures. The main idea was to help researchers and graduate students in mathematics and theoretical physics who encounter graphs in their research to overcome conceptual barriers. The collection begins with Sullivan's paper, "Sigma models and string topology," which describes a background algebraic structure for the sigma model based on algebraic topology and transversality. Other contributions to the volume were organized into five sections: Feynman Diagrams, Algebraic Structures, Manifolds: Invariants and Mirror Symmetry, Combinatorial Aspects of Dynamics, and Physics. These sections, along with more research-oriented articles, contain the following surveys: "Feynman diagrams for pedestrians and mathematicians" by M. Polyak, "Notes on universal algebra" by A. Voronov, "Unimodal maps and hierarchical models" by M. Yampolsky, and "Quantum geometry in action: big bang and black holes" by A. Ashtekar. This comprehensive volume is suitable for graduate students and research mathematicians interested in graph theory and its applications in mathematics and physics.
After several decades of reduced contact, the interaction between physicists and mathematicians in the front-line research of both fields recently became deep and fruit ful again. Many of the leading specialists of both fields became involved in this devel opment. This process even led to the discovery of previously unsuspected connections between various subfields of physics and mathematics. In mathematics this concerns in particular knots von Neumann algebras, Kac-Moody algebras, integrable non-linear partial differential equations, and differential geometry in low dimensions, most im portantly in three and four dimensional spaces. In physics it concerns gravity, string theory, integrable classical and quantum field theories, solitons and the statistical me chanics of surfaces. New discoveries in these fields are made at a rapid pace. This conference brought together active researchers in these areas, reporting their results and discussing with other participants to further develop thoughts in future new directions. The conference was attended by SO participants from 15 nations. These proceedings document the program and the talks at the conference. This conference was preceded by a two-week summer school. Ten lecturers gave extended lectures on related topics. The proceedings of the school will also be published in the NATO-AS[ volume by Plenum. The Editors vii ACKNOWLEDGMENTS We would like to thank the many people who have made the conference a success. Furthermore, ·we appreciate the excellent talks. The active participation of everyone present made the conference lively and stimulating. All of this made our efforts worth while.
