Lectures on Riemann Surfaces

Author: Otto Forster

Publisher: Springer Science & Business Media

ISBN: 1461259614

Category: Mathematics

Page: 256

View: 4596

This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Münster. It provides a concise modern introduction to this rewarding subject, as well as presenting methods used in the study of complex manifolds in the special case of complex dimension one. From the reviews: "This book deserves very serious consideration as a text for anyone contemplating giving a course on Riemann surfaces."—-MATHEMATICAL REVIEWS

Riemann Surfaces

Author: Simon Donaldson

Publisher: Oxford University Press

ISBN: 0198526393

Category: Mathematics

Page: 286

View: 952

An authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view; it pulls together material from global analysis, topology, and algebraic geometry, and covers the essential mathematical methods and tools.

Quanta of Maths

Author: Alain Connes,Institut Henri Poincaré,Institut des hautes études scientifiques (Paris, France),Institut de mathématiques de Jussieu

Publisher: American Mathematical Soc.

ISBN: 0821852035

Category: Mathematics

Page: 675

View: 8543

The work of Alain Connes has cut a wide swath across several areas of mathematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics. Specific themes covered by the articles are as follows: entropy in operator algebras, regular $C^*$-algebras of integral domains, properly infinite $C^*$-algebras, representations of free groups and 1-cohomology, Leibniz seminorms and quantum metric spaces; von Neumann algebras, fundamental Group of $\mathrm{II}_1$ factors, subfactors and planar algebras; Baum-Connes conjecture and property T, equivariant K-homology, Hermitian K-theory; cyclic cohomology, local index formula and twisted spectral triples, tangent groupoid and the index theorem; noncommutative geometry and space-time, spectral action principle, quantum gravity, noncommutative ADHM and instantons, non-compact spectral triples of finite volume, noncommutative coordinate algebras; Hopf algebras, Vinberg algebras, renormalization and combinatorics, motivic renormalization and singularities; cyclotomy and analytic geometry over $F_1$, quantum modular forms; differential K-theory, cyclic theory and S-cohomology.

Tools for PDE

Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials

Author: Michael Eugene Taylor

Publisher: American Mathematical Soc.

ISBN: 0821843788


Page: 257

View: 2202

This book develops three related tools that are useful in the analysis of partial differential equations (PDEs), arising from the classical study of singular integral operators: pseudodifferential operators, paradifferential operators, and layer potentials. A theme running throughout the work is the treatment of PDE in the presence of relatively little regularity. The first chapter studies classes of pseudodifferential operators whose symbols have a limited degree of regularity; the second chapter shows how paradifferential operators yield sharp estimates on the action of various nonlinear operators on function spaces. The third chapter applies this material to an assortment of results in PDE, including regularity results for elliptic PDE with rough coefficients, planar fluid flows on rough domains, estimates on Riemannian manifolds given weak bounds on Ricci tensor, div-curl estimates, and results on propagation of singularities for wave equations with rough coefficients. The last chapter studies the method of layer potentials on Lipschitz domains, concentrating on applications to boundary problems for elliptic PDE with variable coefficients.

From Holomorphic Functions to Complex Manifolds

Author: Klaus Fritzsche,Hans Grauert

Publisher: Springer Science & Business Media

ISBN: 146849273X

Category: Mathematics

Page: 398

View: 9856

This introduction to the theory of complex manifolds covers the most important branches and methods in complex analysis of several variables while completely avoiding abstract concepts involving sheaves, coherence, and higher-dimensional cohomology. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Each chapter contains a variety of examples and exercises.

New Trends in Approximation Theory

In Memory of André Boivin

Author: Javad Mashreghi,Myrto Manolaki,Paul Gauthier

Publisher: Springer

ISBN: 1493975439

Category: Mathematics

Page: 278

View: 1351

The international conference entitled "New Trends in Approximation Theory" was held at the Fields Institute, in Toronto, from July 25 until July 29, 2016. The conference was fondly dedicated to the memory of our unique friend and colleague, André Boivin, who gave tireless service in Canada until his very last moment of his life in October 2014. The impact of his warm personality and his fine work on Complex Approximation Theory was reflected by the mathematical excellence and the wide research range of the 37 participants. In total there were 27 talks, delivered by well-established mathematicians and young researchers. In particular, 19 invited lectures were delivered by leading experts of the field, from 8 different countries. The wide variety of presentations composed a mosaic of aspects of approximation theory, highlighting interesting connections with important contemporary areas of Analysis. Primary topics discussed include application of approximation theory (isoperimetric inequalities, construction of entire order-isomorphisms, dynamical sampling); approximation by harmonic and holomorphic functions (especially uniform and tangential approximation), polynomial and rational approximation; zeros of approximants and zero-free approximation; tools used in approximation theory; approximation on complex manifolds, in product domains, and in function spaces; and boundary behaviour and universality properties of Taylor and Dirichlet series.

GPU Solutions to Multi-scale Problems in Science and Engineering

Author: David A. Yuen,Long Wang,Xuebin Chi,Lennart Johnsson,Wei Ge,Shi Yaolin

Publisher: Springer Science & Business Media

ISBN: 3642164056

Category: Computers

Page: 693

View: 8839

This book covers the new topic of GPU computing with many applications involved, taken from diverse fields such as networking, seismology, fluid mechanics, nano-materials, data-mining , earthquakes ,mantle convection, visualization. It will show the public why GPU computing is important and easy to use. It will offer a reason why GPU computing is useful and how to implement codes in an everyday situation.

Uncertainty-Based Information

Elements of Generalized Information Theory

Author: George Klir,Mark Wierman

Publisher: Physica

ISBN: 3790818690

Category: Mathematics

Page: 168

View: 1547

Information is precious. It reduces our uncertainty in making decisions. Knowledge about the outcome of an uncertain event gives the possessor an advantage. It changes the course of lives, nations, and history itself. Information is the food of Maxwell's demon. His power comes from know ing which particles are hot and which particles are cold. His existence was paradoxical to classical physics and only the realization that information too was a source of power led to his taming. Information has recently become a commodity, traded and sold like or ange juice or hog bellies. Colleges give degrees in information science and information management. Technology of the computer age has provided access to information in overwhelming quantity. Information has become something worth studying in its own right. The purpose of this volume is to introduce key developments and results in the area of generalized information theory, a theory that deals with uncertainty-based information within mathematical frameworks that are broader than classical set theory and probability theory. The volume is organized as follows.

Advances in Iterative Methods for Nonlinear Equations

Author: Sergio Amat,Sonia Busquier

Publisher: Springer

ISBN: 331939228X

Category: Mathematics

Page: 286

View: 3565

This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations, and their approximation.

Introduction to Étale Cohomology

Author: Günter Tamme

Publisher: Springer Science & Business Media

ISBN: 3642784216

Category: Mathematics

Page: 186

View: 5674

A succinct introduction to etale cohomology. Well-presented and chosen this will be a most welcome addition to the algebraic geometrist's library.

The Hermitian Two Matrix Model with an Even Quartic Potential

Author: Maurice Duits,Arno B. J. Kuijlaars,Man Yue Mo

Publisher: American Mathematical Soc.

ISBN: 0821869280

Category: Boundary value problems

Page: 105

View: 9682

The authors consider the two matrix model with an even quartic potential $W(y)=y^4/4+\alpha y^2/2$ and an even polynomial potential $V(x)$. The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices $M_1$. The vector equilibrium problem is defined for three measures, with external fields on the first and third measures and an upper constraint on the second measure. The proof is based on a steepest descent analysis of a $4\times4$ matrix valued Riemann-Hilbert problem that characterizes the correlation kernel for the eigenvalues of $M_1$. The authors' results generalize earlier results for the case $\alpha=0$, where the external field on the third measure was not present.

New Paths Towards Quantum Gravity

Author: Bernhelm Booß-Bavnbek,Maria Rosaria D'Esposito,Matthias Lesch

Publisher: Springer

ISBN: 3642118976

Category: Science

Page: 350

View: 7327

Aside from the obvious statement that it should be a theory capable of unifying general relativity and quantum field theory, not much is known about the true nature of quantum gravity. New ideas - and there are many of them for this is an exciting field of research - often diverge to a degree where it seems impossible to decide in which of the many possible direction(s) the ongoing developments should be further sustained. The division of the book in two (overlapping) parts reflects the duality between the physical vision and the mathematical construction. The former is represented by tutorial reviews on non-commutative geometry, on space-time discretization and renormalization and on gauge field path integrals. The latter one by lectures on cohomology, on stochastic geometry and on mathematical tools for the effective action in quantum gravity. The book will benefit everyone working or entering the field of quantum gravity research.

Teichmüller Theory in Riemannian Geometry

Author: Anthony Tromba

Publisher: Birkhäuser

ISBN: 3034886136

Category: Mathematics

Page: 220

View: 2722

These lecture notes are based on the joint work of the author and Arthur Fischer on Teichmiiller theory undertaken in the years 1980-1986. Since then many of our colleagues have encouraged us to publish our approach to the subject in a concise format, easily accessible to a broad mathematical audience. However, it was the invitation by the faculty of the ETH Ziirich to deliver the ETH N achdiplom-Vorlesungen on this material which provided the opportunity for the author to develop our research papers into a format suitable for mathematicians with a modest background in differential geometry. We also hoped it would provide the basis for a graduate course stressing the application of fundamental ideas in geometry. For this opportunity the author wishes to thank Eduard Zehnder and Jiirgen Moser, acting director and director of the Forschungsinstitut fiir Mathematik at the ETH, Gisbert Wiistholz, responsible for the Nachdiplom Vorlesungen and the entire ETH faculty for their support and warm hospitality. This new approach to Teichmiiller theory presented here was undertaken for two reasons. First, it was clear that the classical approach, using the theory of extremal quasi-conformal mappings (in this approach we completely avoid the use of quasi-conformal maps) was not easily applicable to the theory of minimal surfaces, a field of interest of the author over many years. Second, many other active mathematicians, who at various times needed some Teichmiiller theory, have found the classical approach inaccessible to them.

An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem

Author: Luca Capogna,Donatella Danielli,Scott D. Pauls,Jeremy Tyson

Publisher: Springer Science & Business Media

ISBN: 3764381337

Category: Mathematics

Page: 224

View: 6532

This book gives an up-to-date account of progress on Pansu's celebrated problem on the sub-Riemannian isoperimetric profile of the Heisenberg group. It also serves as an introduction to the general field of sub-Riemannian geometric analysis. It develops the methods and tools of sub-Riemannian differential geometry, nonsmooth analysis, and geometric measure theory suitable for attacks on Pansu's problem.


From Simple to Complex

Author: Alexander Balanov,Natalia Janson,Dmitry Postnov,Olga Sosnovtseva

Publisher: Springer Science & Business Media

ISBN: 3540721282

Category: Science

Page: 426

View: 9987

This fascinating work is devoted to the fundamental phenomenon in physics – synchronization that occurs in coupled non-linear dissipative oscillators. Examples of such systems range from mechanical clocks to population dynamics, from the human heart to neural networks. The main purpose of this book is to demonstrate that the complexity of synchronous patterns of real oscillating systems can be described in the framework of the general approach, and the authors study this phenomenon as applied to oscillations of different types, such as those with periodic, chaotic, noisy and noise-induced nature.

The Palgrave Handbook of Managing Continuous Business Transformation

Author: Horst Ellermann,Peter Kreutter,Wolfgang Messner

Publisher: Springer

ISBN: 1137602287

Category: Business & Economics

Page: 610

View: 3160

This handbook provides a comprehensive and unparalleled reference point for studying continuous business transformation. Asserting that change will be the new normal and highlighting the fact that business transformation can never be complete, this important resource is a tool for coping with ongoing change in order to become and stay resilient, the predominant concern of executives across industries. Containing case study material to illustrate issues and solutions, The Palgrave Handbook of Managing Continuous Business Transformation takes an interdisciplinary approach weaving together strategic concepts with real-life experiences, connecting human resource issues with shifts in information technology and linking customers with the businesses from which they buy. Structured into four parts; transformational shifts, achieving customer centricity, dealing with new technology and leading the change, this handbook is crucial reading for academics, scholars and practitioners of business transformation.

The Cambridge Handbook of Creativity and Personality Research

Author: Gregory J. Feist,Roni Reiter-Palmon,James C. Kaufman

Publisher: Cambridge University Press

ISBN: 1108138632

Category: Psychology

Page: N.A

View: 2394

As individual subjects, creativity and personality have been the focus of much research and many publications. This Cambridge Handbook is the first to bring together these two topics and explores how personality and behavior affects creativity. Contributors from around the globe present cutting-edge research about how personality traits and motives make creative behavior more likely. Many aspects of personality and behavior are examined in the chapters, including genius, emotions, psychopathology, entrepreneurship, and multiculturalism, to analyse the impact of these on creativity. The Cambridge Handbook of Creativity and Personality Research will be the definitive resource for researchers, students and academics who study psychology, personality, and creativity.

Non-Euclidean Geometries

János Bolyai Memorial Volume

Author: András Prékopa,Emil Molnár

Publisher: Springer Science & Business Media

ISBN: 0387295550

Category: Mathematics

Page: 506

View: 863

"From nothing I have created a new different world," wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.