Download or read book Arithmetic Geometry written by Jean-Louis Colliot-Thélène and published by Springer. This book was released on 2010-10-27 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties through arbitrary rings, in particular through non-algebraically closed fields. It lies at the intersection between classical algebraic geometry and number theory. A C.I.M.E. Summer School devoted to arithmetic geometry was held in Cetraro, Italy in September 2007, and presented some of the most interesting new developments in arithmetic geometry. This book collects the lecture notes which were written up by the speakers. The main topics concern diophantine equations, local-global principles, diophantine approximation and its relations to Nevanlinna theory, and rationally connected varieties. The book is divided into three parts, corresponding to the courses given by J-L Colliot-Thelene, Peter Swinnerton Dyer and Paul Vojta.

Download or read book Intersection Spaces Spatial Homology Truncation and String Theory written by Markus Banagl and published by Springer. This book was released on 2010-06-16 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space. This monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality. The cornerstone of the method is a process of spatial homology truncation, whose functoriality properties are analyzed in detail. The material on truncation is autonomous and may be of independent interest tohomotopy theorists. The cohomology of intersection spaces is not isomorphic to intersection cohomology and possesses algebraic features such as perversity-internal cup-products and cohomology operations that are not generally available for intersection cohomology. A mirror-symmetric interpretation, as well as applications to string theory concerning massless D-branes arising in type IIB theory during a Calabi-Yau conifold transition, are discussed.

Download or read book Geometry of M ntz Spaces and Related Questions written by Vladimir I. Gurariy and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Symmetries of Compact Riemann Surfaces written by Emilio Bujalance and published by Springer Science & Business Media. This book was released on 2010-10-06 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with symmetries of compact Riemann surfaces. A symmetry of a compact Riemann surface S is an antianalytic involution of S. It is well known that Riemann surfaces exhibiting symmetry correspond to algebraic curves which can be defined over the field of real numbers. In this monograph we consider three topics related to the topology of symmetries, namely the number of conjugacy classes of symmetries, the numbers of ovals of symmetries and the symmetry types of Riemann surfaces.

Download or read book The Ricci Flow in Riemannian Geometry written by Ben Andrews and published by Springer Science & Business Media. This book was released on 2011 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.

Download or read book Geometric Theory of Discrete Nonautonomous Dynamical Systems written by Christian Pötzsche and published by Springer. This book was released on 2010-08-24 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to have attractors using the natural concept of pullback convergence. Concerning a necessary linear theory, our hyperbolicity concept is based on exponential dichotomies and splittings. This concept is in turn used to construct nonautonomous invariant manifolds, so-called fiber bundles, and deduce linearization theorems. The results are illustrated using temporal and full discretizations of evolutionary differential equations.

Download or read book Lebesgue and Sobolev Spaces with Variable Exponents written by Lars Diening and published by Springer. This book was released on 2011-03-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.

Download or read book Computational Approach to Riemann Surfaces written by Alexander I. Bobenko and published by Springer Science & Business Media. This book was released on 2011-02-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.

Download or read book Some Mathematical Models from Population Genetics written by Alison Etheridge and published by Springer Science & Business Media. This book was released on 2011-01-07 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some, like the classical Wright-Fisher model, date right back to the origins of the subject. Others, like the multiple merger coalescents or the spatial Lambda-Fleming-Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained, the models are carefully motivated and tools for their study are presented systematically.

Download or read book The Analysis of Fractional Differential Equations written by Kai Diethelm and published by Springer Science & Business Media. This book was released on 2010-09-03 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Download or read book Advanced Courses of Mathematical Analysis II written by M. V. Velasco and published by World Scientific. This book was released on 2007 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises a collection of articles by leading researchers in mathematical analysis. It provides the reader with an extensive overview of new directions and advances in topics for current and future research in the field. Contents: Lineable and Spaceable Properties (R M Aron); Alexander Grothendieck's Work on Functional Analysis (F Bombal); Maximal Functions in Fourier Analysis (J Duoandikoetxea); Hypercyclic Operators: Some Recent Progress (G Godefroy); On the Hahn-Banach Theorem (L Narici); Lipschitz Quotient Maps Between Banach Spaces (W B Johnson); Approximation Algorithms in Banach Spaces (N Kalton); Spectral Properties of Cesa'ro-Like Operators (M M Neumann); Some Ideas on Mathematical Training Concerning Mathematical Analysis (B Rubio); Interpolation and Sampling (K Seip); Classes of Indefinitely Differentiable Functions (M Valdivia); Classical Potential Theory and Analytic Capacity (J Verdera); Best Approximations on Small Regions: A General Approach (F Zo & H H Cuenya). Readership: Mathematicians in analysis and differential equations and approximation theory.

Download or read book Advanced Courses Of Mathematical Analysis Ii Proceedings Of The Second International School written by M Victoria Velasco and published by World Scientific. This book was released on 2007-03-22 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises a collection of articles by leading researchers in mathematical analysis. It provides the reader with an extensive overview of new directions and advances in topics for current and future research in the field.

Download or read book Mutational Analysis written by Thomas Lorenz and published by Springer Science & Business Media. This book was released on 2010-06-08 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary differential equations have been extended to evolution equations in Banach spaces. This book generalizes ordinary differential equations beyond the borders of vector spaces with a focus on the well-posed Cauchy problem in finite time intervals.

Download or read book L vy Matters I written by Thomas Duquesne and published by Springer Science & Business Media. This book was released on 2010-09-05 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the breadth of the topic, this volume explores Lévy processes and applications, and presents the state-of-the-art in this evolving area of study. These expository articles help to disseminate important theoretical and applied research to those studying the field.

Download or read book The Use of Ultraproducts in Commutative Algebra written by Hans Schoutens and published by Springer. This book was released on 2010-07-16 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: In spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make a strong case against these prejudices. More precisely, it studies ultraproducts of Noetherian local rings from a purely algebraic perspective, as well as how they can be used to transfer results between the positive and zero characteristics, to derive uniform bounds, to define tight closure in characteristic zero, and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants called chromatic products, which are often even Noetherian. This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra.

Download or read book Holomorphic Dynamical Systems written by Nessim Sibony and published by Springer Science & Business Media. This book was released on 2010-07-31 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector ?eld) acting on it. The study of a holomorphic dynamical system consists in describing the asymptotic behavior of the system, associating it with some invariant objects (easy to compute) which describe the dynamics and classify the possible holomorphic dynamical systems supported by a given manifold. The behavior of a holomorphic dynamical system is pretty much related to the geometry of the ambient manifold (for instance, - perbolic manifolds do no admit chaotic behavior, while projective manifolds have a variety of different chaotic pictures). The techniques used to tackle such pr- lems are of variouskinds: complexanalysis, methodsof real analysis, pluripotential theory, algebraic geometry, differential geometry, topology. To cover all the possible points of view of the subject in a unique occasion has become almost impossible, and the CIME session in Cetraro on Holomorphic Dynamical Systems was not an exception.

Download or read book Fatou Julia Montel written by Michèle Audin and published by Springer Science & Business Media. This book was released on 2011-01-30 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: How did Pierre Fatou and Gaston Julia create what we now call Complex Dynamics, in the context of the early twentieth century and especially of the First World War? The book is based partly on new, unpublished sources. Who were Pierre Fatou, Gaston Julia, Paul Montel? New biographical information is given on the little known mathematician that was Pierre Fatou. How did the WW1 injury of Julia influence mathematical life in France? From the reviews of the French version: "Audin’s book is ... filled with marvelous biographical information and analysis, dealing not just with the men mentioned in the book’s title but a large number of other players, too ... [It] addresses itself to scholars for whom the history of mathematics has a particular resonance and especially to mathematicians active, or even with merely an interest, in complex dynamics. ... presents it all to the reader in a very appealing form." (Michael Berg, The Mathematical Association of America, October 2009)