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Deformation Quantization
This book contains eleven refereed research papers on deformation quantization by leading experts in the respective fields. These contributions are based on talks presented on the occasion of the meeting between mathematicians and theoretical physicists held in Strasbourg in May 2001. Topics covered are: star-products over Poisson manifolds, quantization of Hopf algebras, index theorems, globalization and cohomological problems. Both the mathematical and the physical approach ranging from asymptotic quantum electrodynamics to operads and prop theory will be presented. Historical remarks and surveys set the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume will give an overview of a field of research that has seen enourmous acticity in the last years, with new ties to many other areas of mathematics and physics.
Mathematics, Developmental Biology and Tumour Growth
Developmental biology and tumour growth are two important areas of current research where mathematics increasingly provides powerful new techniques and insights. The unfolding complexity of living structures from egg to embryo gives rise to a number of difficult quantitative problems that are ripe for mathematical models and analysis. Understanding this early development process involves the study of pattern formation, which mathematicians view through the lens of dynamical systems. This book addresses several issues in developmental biology, including Notch signalling pathway integration and mesenchymal compartment formation. Tumour growth is one of the primary challenges of cancer research. Its study requires interdisciplinary approaches involving the close collaboration of mathematicians, biologists and physicians. The summer school addressed angiogenesis, modelling issues arising in radiotherapy, and tumour growth viewed from the individual cell and the relation to a multiphase-fluid flow picture of that process. This book is suitable for researchers, graduate students, and advanced undergraduates interested in mathematical methods of developmental biology or tumour growth.
Computational Group Theory and the Theory of Groups
"The power of general purpose computational algebra systems running on personal computers has increased rapidly in recent years. For mathematicians doing research in group theory, this means a growing set of sophisticated computational tools are now available for their use in developing new theoretical results." "This volume consists of contributions by researchers invited to the AMS Special Session on Computational Group Theory held in March 2007. The main focus of the session was on the application of Computational Group Theory (CGT) to a wide range of theoretical aspects of group theory. The articles in this volume provide a variety of examples of how these computer systems helped to solv...
The Universe
This volume provides a detailed description of some of the most active areas in astrophysics from the largest scales probed by the Planck satellite to massive black holes that lie at the heart of galaxies and up to the much awaited but stunning discovery of thousands of exoplanets. It contains the following chapters: • Jean-Philippe UZAN, The Big-Bang Theory: Construction, Evolution and Status • Jean-Loup PUGET, The Planck Mission and the Cosmic Microwave Background • Reinhard GENZEL, Massive Black Holes: Evidence, Demographics and Cosmic Evolution • Arnaud CASSAN, New Worlds Ahead: The Discovery of Exoplanets Reinhard Genzel and Andrea Ghez shared the 2020 Nobel Prize in Physics “...
Hopf Algebras in Noncommutative Geometry and Physics
This comprehensive reference summarizes the proceedings and keynote presentations from a recent conference held in Brussels, Belgium. Offering 1155 display equations, this volume contains original research and survey papers as well as contributions from world-renowned algebraists. It focuses on new results in classical Hopf algebras as well as the
Noncommutative Geometry And Physics - Proceedings Of The Coe International Workshop
Noncommutative differential geometry is a novel approach to geometry that is paving the way for exciting new directions in the development of mathematics and physics. The contributions in this volume are based on papers presented at a workshop dedicated to enhancing international cooperation between mathematicians and physicists in various aspects of frontier research on noncommutative differential geometry. The active contributors present both the latest results and comprehensive reviews of topics in the area. The book is accessible to researchers and graduate students interested in a variety of mathematical areas related to noncommutative geometry and its interface with modern theoretical physics.
Topics in Mathematical Physics, General Relativity, and Cosmology in Honor of Jerzy Pleba?ski
One of modern science's most famous and controversial figures, Jerzy Plebanski was an outstanding theoretical physicist and an author of many intriguing discoveries in general relativity and quantum theory. Known for his exceptional analytic talents, explosive character, inexhaustible energy, and bohemian nights with brandy, coffee, and enormous amounts of cigarettes, he was dedicated to both science and art, producing innumerable handwritten articles - resembling monk's calligraphy - as well as a collection of oil paintings. As a collaborator but also an antagonist of Leopold Infeld's (a coauthor of Albert Einstein's), Plebanski is recognized for designing the "heavenly" and "hyper-heavenly...
Functional Analysis and Complex Analysis
In recent years, the interplay between the methods of functional analysis and complex analysis has led to some remarkable results in a wide variety of topics. It turned out that the structure of spaces of holomorphic functions is fundamentally linked to certain invariants initially defined on abstract Frechet spaces as well as to the developments in pluripotential theory. The aim of this volume is to document some of the original contributions to this topic presented at a conference held at Sabanci University in Istanbul, in September 2007. This volume also contains some surveys that give an overview of the state of the art and initiate further research in the interplay between functional and complex analysis.
Rigorous Time Slicing Approach to Feynman Path Integrals
This book proves that Feynman's original definition of the path integral actually converges to the fundamental solution of the Schrödinger equation at least in the short term if the potential is differentiable sufficiently many times and its derivatives of order equal to or higher than two are bounded. The semi-classical asymptotic formula up to the second term of the fundamental solution is also proved by a method different from that of Birkhoff. A bound of the remainder term is also proved.The Feynman path integral is a method of quantization using the Lagrangian function, whereas Schrödinger's quantization uses the Hamiltonian function. These two methods are believed to be equivalent. B...
