%{search_type} search results

• Preface-- List of contributors--
• 1. A semi-stable case of the Shafarevich conjecture V. Abrashkin--
• 2. Irreducible modular representations of the Borel subgroup of GL2(Qp) L. Berger and M. Vienney--
• 3. p-adic L-functions and Euler systems: a tale in two trilogies M. Bertolini, F. Castella, H. Darmon, S. Dasgupta, K. Prasanna and V. Rotger--
• 4. Effective local Langlands correspondence C. J. Bushnell--
• 5. The conjectural connections between automorphic representations and Galois representations K. Buzzard and T. Gee--
• 6. Geometry of the fundamental lemma P.-H. Chaudouard--
• 7. The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings G. Chenevier--
• 8. La serie principale unitaire de GL2(Qp): vecteurs localement analytiques P. Colmez--
• 9. Equations differentielles p-adiques et modules de Jacquet analytiques G. Dospinescu.
• (source: Nielsen Book Data)

• Preface-- List of contributors--
• 1. On the local structure of ordinary Hecke algebras at classical weight one points M. Dimitrov--
• 2. Vector bundles on curves and p-adic Hodge theory L. Fargues and J.-M. Fontaine--
• 3. Around associators H. Furusho--
• 4. The stable Bernstein center and test function for Shimura varieties T. J. Haines--
• 5. Conditional results on the birational section conjecture over small number fields Y. Hoshi--
• 6. Blocks for mod p representations of GL2(Qp) V. Paskunas--
• 7. From etale P+-representations to G-equivariant sheaves on G/P P. Schneider, M.-F. Vigneras and G. Zabradi--
• 8. Intertwining of ramified and unramified zeros of Iwasawa modules C. Khare and J.-P. Wintenberger.
• (source: Nielsen Book Data)

Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wiles' proof of Fermat's Last Theorem. This two-volume collection arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic Forms and Galois Representations' in July 2011, the aim of which was to explore recent developments in this area. The expository articles and research papers across the two volumes reflect recent interest in p-adic methods in number theory and representation theory, as well as recent progress on topics from anabelian geometry to p-adic Hodge theory and the Langlands program. The topics covered in volume two include curves and vector bundles in p-adic Hodge theory, associators, Shimura varieties, the birational section conjecture, and other topics of contemporary interest.
(source: Nielsen Book Data)

• Preface--
• 1. Hyperbolic geometry A. Aigon-Dupuy, P. Buser and K.-D. Semmler--
• 2. Selberg's trace formula: an introduction J. Marklof--
• 3. Semiclassical approach to spectral correlation functions M. Sieber--
• 4. Transfer operators, the Selberg Zeta function and the Lewis-Zagier theory of period functions D. H. Mayer--
• 5. On the calculation of Maass cusp forms D. A. Hejhal--
• 6. Maass waveforms on ( 0(N), x) (computational aspects) Fredrik Stroemberg--
• 7. Numerical computation of Maass waveforms and an application to cosmology R. Aurich, F. Steiner and H. Then.
• (source: Nielsen Book Data)

Hyperbolic geometry is a classical subject in pure mathematics which has exciting applications in theoretical physics. In this book leading experts introduce hyperbolic geometry and Maass waveforms and discuss applications in quantum chaos and cosmology. The book begins with an introductory chapter detailing the geometry of hyperbolic surfaces and includes numerous worked examples and exercises to give the reader a solid foundation for the rest of the book. In later chapters the classical version of Selberg's trace formula is derived in detail and transfer operators are developed as tools in the spectral theory of Laplace-Beltrami operators on modular surfaces. The computation of Maass waveforms and associated eigenvalues of the hyperbolic Laplacian on hyperbolic manifolds are also presented in a comprehensive way. This book will be valuable to graduate students and young researchers, as well as for those experienced scientists who want a detailed exposition of the subject.
(source: Nielsen Book Data)

• List of contributors-- Preface--
• 1. Lectures on anabelian phenomena in geometry and arithmetic Florian Pop--
• 2. On Galois rigidity of fundamental groups of algebraic curves Hiroaki Nakamura--
• 3. Around the Grothendieck anabelian section conjecture Mohamed Saidi--
• 4. From the classical to the noncommutative Iwasawa theory (for totally real number fields) Mahesh Kakde--
• 5. On the MUH(G)-conjecture J. Coates and R. Sujatha--
• 6. Galois theory and Diophantine geometry Minhyong Kim--
• 7. Potential modularity - a survey Kevin Buzzard--
• 8. Remarks on some locally Qp-analytic representations of GL2(F) in the crystalline case Christophe Breuil--
• 9. Completed cohomology - a survey Frank Calegari and Matthew Emerton--
• 10. Tensor and homotopy criteria for functional equations of l-adic and classical iterated integrals Hiroaki Nakamura and Zdzislaw Wojtkowiak.
• (source: Nielsen Book Data)

Number theory currently has at least three different perspectives on non-abelian phenomena: the Langlands programme, non-commutative Iwasawa theory and anabelian geometry. In the second half of 2009, experts from each of these three areas gathered at the Isaac Newton Institute in Cambridge to explain the latest advances in their research and to investigate possible avenues of future investigation and collaboration. For those in attendance, the overwhelming impression was that number theory is going through a tumultuous period of theory-building and experimentation analogous to the late 19th century, when many different special reciprocity laws of abelian class field theory were formulated before knowledge of the Artin-Takagi theory. Non-abelian Fundamental Groups and Iwasawa Theory presents the state of the art in theorems, conjectures and speculations that point the way towards a new synthesis, an as-yet-undiscovered unified theory of non-abelian arithmetic geometry.
(source: Nielsen Book Data)

• Introduction--
• 1. Introduction to fusion systems--
• 2. The local theory of fusion systems--
• 3. Fusion and homotopy theory--
• 4. Fusion and representation theory-- Appendix. Background facts about groups-- References-- List of notation-- Index.
• (source: Nielsen Book Data)

A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.
(source: Nielsen Book Data)

• Preface--
• 1. Introduction--
• 2. Background results in representation theory--
• 3. Representations of SO(3) and harmonic analysis on S2--
• 4. Background results in probability and graphical methods--
• 5. Spectral representations--
• 6. Characterizations of isotropy--
• 7. Limit theorems for Gaussian subordinated random fields--
• 8. Asymptotics for the sample power spectrum--
• 9. Asymptotics for sample bispectra--
• 10. Spherical needlets and their asymptotic properties--
• 11. Needlets estimation of power spectrum and bispectrum--
• 12. Spin random fields-- Appendix-- Bibliography-- Index.
• (source: Nielsen Book Data)

Random Fields on the Sphere presents a comprehensive analysis of isotropic spherical random fields. The main emphasis is on tools from harmonic analysis, beginning with the representation theory for the group of rotations SO(3). Many recent developments on the method of moments and cumulants for the analysis of Gaussian subordinated fields are reviewed. This background material is used to analyse spectral representations of isotropic spherical random fields and then to investigate in depth the properties of associated harmonic coefficients. Properties and statistical estimation of angular power spectra and polyspectra are addressed in full. The authors are strongly motivated by cosmological applications, especially the analysis of cosmic microwave background (CMB) radiation data, which has initiated a challenging new field of mathematical and statistical research. Ideal for mathematicians and statisticians interested in applications to cosmology, it will also interest cosmologists and mathematicians working in group representations, stochastic calculus and spherical wavelets.
(source: Nielsen Book Data)

• 1. Lagrangian and Hamiltonian formalism for discrete equations: symmetries and first integrals V. Dorodnitsyn and R. Kozlov--
• 2. Painleve equations: continuous, discrete and ultradiscrete B. Grammaticos and A. Ramani--
• 3. Definitions and predictions of integrability for difference equations J. Hietarinta--
• 4. Orthogonal polynomials, their recursions, and functional equations M. E. H. Ismail--
• 5. Discrete Painleve equations and orthogonal polynomials A. Its--
• 6. Generalized Lie symmetries for difference equations D. Levi and R. I. Yamilov--
• 7. Four lectures on discrete systems S. P. Novikov--
• 8. Lectures on moving frames P. J. Olver--
• 9. Lattices of compact semisimple Lie groups J. Patera--
• 10. Lectures on discrete differential geometry Yu. B Suris--
• 11. Symmetry preserving discretization of differential equations and Lie point symmetries of differential-difference equations P. Winternitz.
• (source: Nielsen Book Data)

Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover, in their study it is very often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference equations. This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference ones. Each of the eleven chapters is a self-contained treatment of a topic, containing introductory material as well as the latest research results. The book will be welcomed by graduate students and researchers seeking an introduction to the field. As a survey of the current state of the art it will also serve as a valuable reference.
(source: Nielsen Book Data)

• Preface--
• 1. Introduction--
• 2. Metrics and frames--
• 3. Computing with frames--
• 4. Energy inequalities and frames--
• 5. The good components--
• 6. Pointwise estimates and commutations--
• 7. Frames and curvature--
• 8. Nonlinear equations, a priori estimates and induction--
• 9. Applications to some quasilinear hyperbolic problems-- References-- Index.
• (source: Nielsen Book Data)

Its self-contained presentation and 'do-it-yourself' approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of nonlinear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics, null frames, deformation tensors, etc.) and provides complete elementary proofs. The author also discusses applications to topics in nonlinear equations, including null conditions and stability of Minkowski space. No previous knowledge of geometry or relativity is required.
(source: Nielsen Book Data)

• Foreword Jean-Pierre Tignol-- Introduction-- Part I. An Introduction to Galois Cohomology:
• 1. Infinite Galois theory--
• 2. Cohomology of profinite groups--
• 3. Galois cohomology--
• 4. Galois cohomology of quadratic forms--
• 5. Etale and Galois algebras--
• 6. Groups extensions and Galois embedding problems-- Part II. Applications:
• 7. Galois embedding problems and the trace form--
• 8. Galois cohomology of central simple algebras--
• 9. Digression: a geometric interpretation of H1 (-, G)--
• 10. Galois cohomology and Noether's problem--
• 11. The rationality problem for adjoint algebraic groups--
• 12. Essential dimension of functors-- References-- Index.
• (source: Nielsen Book Data)

This is the first elementary introduction to Galois cohomology and its applications. The first part is self-contained and provides the basic results of the theory, including a detailed construction of the Galois cohomology functor, as well as an exposition of the general theory of Galois descent. The author illustrates the theory using the example of the descent problem of conjugacy classes of matrices. The second part of the book gives an insight into how Galois cohomology may be used to solve algebraic problems in several active research topics, such as inverse Galois theory, rationality questions or the essential dimension of algebraic groups. Assuming only a minimal background in algebra, the main purpose of this book is to prepare graduate students and researchers for more advanced study.
(source: Nielsen Book Data)

• Preface--
• 1. Introduction--
• 2. Graph operations and modifications--
• 3. Spectrum and structure--
• 4. Characterizations by spectra--
• 5. Structure and one eigenvalue--
• 6. Spectral techniques--
• 7. Laplacians--
• 8. Additional topics--
• 9. Applications-- Appendix-- Bibliography-- Index of symbols-- Index.
• (source: Nielsen Book Data)

This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined here are those of the adjacency matrix, the Seidel matrix, the Laplacian, the normalized Laplacian and the signless Laplacian of a finite simple graph. The underlying theme of the book is the relation between the eigenvalues and structure of a graph. Designed as an introductory text for graduate students, or anyone using the theory of graph spectra, this self-contained treatment assumes only a little knowledge of graph theory and linear algebra. The authors include many new developments in the field which arise as a result of rapidly expanding interest in the area. Exercises, spectral data and proofs of required results are also provided. The end-of-chapter notes serve as a practical guide to the extensive bibliography of over 500 items.
(source: Nielsen Book Data)

• Preface--
• 1. Galois theory of linear differential equations Michael F. Singer--
• 2. Solving in closed form Felix Ulmer and Jacques-Arthur Weil--
• 3. Factorization of linear systems Sergey P. Tsarev--
• 4. Introduction to D-modules Anton Leykin--
• 5. Symbolic representation and classification of integrable systems A. V. Mikhailov, V. S. Novikov and Jing Ping Wang--
• 6. Searching for integrable (P)DEs Jarmo Hietarinta--
• 7. Around differential Galois theory Anand Pillay.
• (source: Nielsen Book Data)

Integration of differential equations is a central problem in mathematics and several approaches have been developed by studying analytic, algebraic, and algorithmic aspects of the subject. One of these is Differential Galois Theory, developed by Kolchin and his school, and another originates from the Soliton Theory and Inverse Spectral Transform method, which was born in the works of Kruskal, Zabusky, Gardner, Green and Miura. Many other approaches have also been developed, but there has so far been no intersection between them. This unique introduction to the subject finally brings them together, with the aim of initiating interaction and collaboration between these various mathematical communities. The collection includes a LMS Invited Lecture Course by Michael F. Singer, together with some shorter lecture courses and review articles, all based upon a mini-programme held at the International Centre for Mathematical Sciences (ICMS) in Edinburgh.
(source: Nielsen Book Data)

The name Central Limit Theorem covers a wide variety of results involving the determination of necessary and sufficient conditions under which sums of independent random variables, suitably standardized, have cumulative distribution functions close to the Gaussian distribution. As the name Central Limit Theorem suggests, it is a centerpiece of probability theory which also carries over to statistics. Part One of "The Life and Times of the Central Limit Theorem, Second Edition" traces its fascinating history from seeds sown by Jacob Bernoulli to use of integrals of exp(x2) as an approximation tool, the development of the theory of errors of observation, problems in mathematical astronomy, the emergence of the hypothesis of elementary errors, the fundamental work of Laplace, and the emergence of an abstract Central Limit Theorem through the work of Chebyshev, Markov and Lyapunov. This closes the classical period of the life of the Central Limit Theorem, 1713-1901. The second part of the book includes papers by Feller and Le Cam, as well as comments by Doob, Trotter, and Pollard, describing the modern history of the Central Limit Theorem (1920-1937), in particular through contributions of Lindeberg, Cramer, Levy, and Feller. The Appendix to the book contains four fundamental papers by Lyapunov on the Central Limit Theorem, made available in English for the first time.
(source: Nielsen Book Data)

• Introduction--
• 1. Metric Measure spaces--
• 2. Lie groups and matrix ensembles--
• 3. Entropy and concentration of measure--
• 4. Free entropy and equilibrium--
• 5. Convergence to equilibrium--
• 6. Gradient ows and functional inequalities--
• 7. Young tableaux--
• 8. Random point fields and random matrices--
• 9. Integrable operators and differential equations--
• 10. Fluctuations and the Tracy-Widom distribution--
• 11. Limit groups and Gaussian measures--
• 12. Hermite polynomials--
• 13. From the Ornstein-Uhlenbeck process to Burger's equation--
• 14. Noncommutative probability spaces-- References-- Index.
• (source: Nielsen Book Data)

This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium.
(source: Nielsen Book Data)

• Preface--
• 1. Fourier series--
• 2. Abel-Poisson means--
• 3. Harmonic functions in the unit disc--
• 4. Logarithmic convexity--
• 5. Analytic functions in the unit disc--
• 6. Norm inequalities for the conjugate function--
• 7. Blaschke products and their applications--
• 8. Interpolating linear operators--
• 9. The Fourier transform--
• 10. Poisson integrals--
• 11. Harmonic functions in the upper half plane--
• 12. The Plancherel transform--
• 13. Analytic functions in the upper half plane--
• 14. The Hilbert transform on R-- A. Topics from real analysis-- B. A panoramic view of the representation theorems-- Bibliography-- Index.
• (source: Nielsen Book Data)

The theory of Hardy spaces has close connections to many branches of mathematics including Fourier analysis, harmonic analysis, singular integrals, potential theory and operator theory, and has found essential applications in robust control engineering. For each application, the ability to represent elements of these classes by series or integral formulas is of utmost importance. This self-contained text provides an introduction to a wide range of representation theorems and provides a complete description of the representation theorems with direct proofs for both classes of Hardy spaces: Hardy spaces of the open unit disc and Hardy spaces of the upper half plane. With over 300 exercises, many with accompanying hints, this book is ideal for those studying Advanced Complex Analysis, Function Theory or Theory of Hardy Spaces. Advanced undergraduate and graduate students will find the book easy to follow, with a logical progression from basic theory to advanced research.
(source: Nielsen Book Data)

• Preface-- Part I. Foundations and techniques in stochastic analysis:
• 1. Random variables - without basic space Goetz Kersting--
• 2. Chaining techniques and their application to stochastic flows Michael Scheutzow--
• 3. Ergodic properties of a class of non-Markovian processes Martin Hairer--
• 4. Why study multifractal spectra? Peter Moerters-- Part II. Construction, simulation, discretisation of stochastic processes: 5, Construction of surface measures for Brownian motion Nadia Sidorova and Olaf Wittich--
• 6. Sampling conditioned diffusions Martin Hairer, Andrew Stuart and Jochen Vo
• 7. Coding and convex optimization problems Steffen Dereich-- Part III. Stochastic analysis in mathematical physics:
• 8. Intermittency on catalysts Jurgen Gartner, Frank den Hollander and Gregory Maillard--
• 9. Stochastic dynamical systems in infinite dimensions Salah-Eldin A. Mohammed--
• 10. Feynman formulae for evolutionary equations Oleg G.Smolyanov--
• 11. Deformation quantization in infinite dimensional analysis Remi Leandre-- Part IV. Stochastic analysis in mathematical biology:
• 12. Measure-valued diffusions, coalescents and genetic inference Matthias Birkner and Jochen Blath--
• 13. How often does the ratchet click? Facts, heuristics, asymptotics Alison M. Etheridge, Peter Pfaffelhuber and Anton Wakolbinger.
• (source: Nielsen Book Data)

Presenting important trends in the field of stochastic analysis, this collection of thirteen articles provides an overview of recent developments and new results. Written by leading experts in the field, the articles cover a wide range of topics, ranging from an alternative set-up of rigorous probability to the sampling of conditioned diffusions. Applications in physics and biology are treated, with discussion of Feynman formulas, intermittency of Anderson models and genetic inference. A large number of the articles are topical surveys of probabilistic tools such as chaining techniques, and of research fields within stochastic analysis, including stochastic dynamics and multifractal analysis. Showcasing the diversity of research activities in the field, this book is essential reading for any student or researcher looking for a guide to modern trends in stochastic analysis and neighbouring fields.
(source: Nielsen Book Data)

• Introduction-- Part I. Basics on Differential Geometry:
• 1. Smooth manifolds--
• 2. Tensor fields on smooth manifolds--
• 3. The exterior derivative--
• 4. Principal and vector bundles--
• 5. Connections--
• 6. Riemannian manifolds-- Part II. Complex and Hermitian Geometry:
• 7. Complex structures and holomorphic maps--
• 8. Holomorphic forms and vector fields--
• 9. Complex and holomorphic vector bundles--
• 10. Hermitian bundles--
• 11. Hermitian and Kahler metrics--
• 12. The curvature tensor of Kahler manifolds--
• 13. Examples of Kahler metrics--
• 14. Natural operators on Riemannian and Kahler manifolds--
• 15. Hodge and Dolbeault theory-- Part III. Topics on Compact Kahler Manifolds:
• 16. Chern classes--
• 17. The Ricci form of Kahler manifolds--
• 18. The Calabi-Yau theorem--
• 19. Kahler-Einstein metrics--
• 20. Weitzenboeck techniques--
• 21. The Hirzebruch-Riemann-Roch formula--
• 22. Further vanishing results--
• 23. Ricci-flat Kahler metrics--
• 24. Explicit examples of Calabi-Yau manifolds-- Bibliography-- Index.
• (source: Nielsen Book Data)

Kahler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kahler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kahler identities. The final part of the text studies several aspects of compact Kahler manifolds: the Calabi conjecture, Weitzenboeck techniques, Calabi-Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.
(source: Nielsen Book Data)

• Preface-- List of participants--
• 1. Stark-Heegner points and special values of L-series Massimo Bertolini, Henri Darmon and Samit Dasgupta--
• 2. Presentations of universal deformation rings Gebhard Bockle-- Eigenvarieties Kevin Buzzard--
• 3. Nontriviality of Rankin-Selberg L-functions and CM points Christophe Cornut and Vinayak Vatsal--
• 4. A correspondence between representations of local Galois groups and Lie-type groups Fred Diamond--
• 5. Non-vanishing modulo p of Hecke L-values and application Haruzo Hida--
• 6. Serre's modularity conjecture: a survey of the level one case Chandrashekhar Khare--
• 7. Two p-adic L-functions and rational points on elliptic curves with supersingular reduction Masato Kurihara and Robert Pollack--
• 8. From the Birch and Swinnerton-Dyer Conjecture to non-commutative Iwasawa theory via the Equivariant Tamagawa Number Conjecture - a survey Otmar Venjakob--
• 9. The Andre-Oort conjecture - a survey Andrei Yafaev--
• 10. Locally analytic representation theory of p-adic reductive groups: a summary of some recent developments Matthew Emerton--
• 11. Modularity for some geometric Galois representations - with an appendix by Ofer Gabber Mark Kisin--
• 12. The Euler system method for CM points on Shimura curves Jan Nekova
• 13. Representations irreductibles de GL(2, F ) modulo p Marie-France Vigneras.
• (source: Nielsen Book Data)

This collection of survey and research articles brings together topics at the forefront of the theory of L-functions and Galois representations. Highlighting important progress in areas such as the local Langlands programme, automorphic forms and Selmer groups, this timely volume treats some of the most exciting recent developments in the field. Included are survey articles from Khare on Serre's conjecture, Yafaev on the Andre-Oort conjecture, Emerton on his theory of Jacquet functors, Venjakob on non-commutative Iwasawa theory and Vigneras on mod p representations of GL(2) over p-adic fields. There are also research articles by: Bockle, Buzzard, Cornut and Vatsal, Diamond, Hida, Kurihara and R. Pollack, Kisin, Nekova , and Bertolini, Darmon and Dasgupta. Presenting the very latest research on L-functions and Galois representations, this volume is indispensable for researchers in algebraic number theory.
(source: Nielsen Book Data)