Books in the Lecture Notes in Mathematics series

This book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation. Spectral data for such solutions are defined (following ideas of Hitchin and Bobenko) and the space of spectral data is described by an asymptotic characterization.

This book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic continuation and functional equation of automorphic L-functions.Developing a general framework that could accommodate Schwartz spaces and the corresponding zeta integrals, the author establishes a formalism, states desiderata and conjectures, draws implications from these assumptions, and shows how known examples fit into this framework, supporting Sakellaridis' vision of the subject. The collected results, both old and new, and the included extensive bibliography, will be valuable to anyone who wishes to understand this program, and to those who are already working on it and want to overcome certain frequently occurring technical difficulties.

It assembles together expository articles on topics which previously could only be found in research papers.Starting with a very detailed article by P.

This book is concerned with several elliptic and parabolic obstacle-type problems with a focus on the cases where the free and fixed boundaries meet. The results presented complement those found in existing books in the subject, which mainly treat regularity properties away from the fixed boundary.The topics include optimal regularity, analysis of global solutions, tangential touch of the free and fixed boundaries, as well as Lipschitz- and $C^1$-regularity of the free boundary. Special attention is given to local versions of various monotonicity formulas.The intended audience includes research mathematicians and advanced graduate students interested in problems with free boundaries.

This book presents tools and methods for large-scale and distributed optimization. Since many methods in "Big Data" fields rely on solving large-scale optimization problems, often in distributed fashion, this topic has over the last decade emerged to become very important. As well as specific coverage of this active research field, the book serves as a powerful source of information for practitioners as well as theoreticians.Large-Scale and Distributed Optimization is a unique combination of contributions from leading experts in the field, who were speakers at the LCCC Focus Period on Large-Scale and Distributed Optimization, held in Lund, 14th-16th June 2017. A source of information and innovative ideas for current and future research, this book will appeal to researchers, academics, and students who are interested in large-scale optimization.

This monograph concerns the relationship between the local spectral theory and Fredholm theory of bounded linear operators acting on Banach spaces. The purpose of this book is to provide a first general treatment of the theory of operators for which Weyl-type or Browder-type theorems hold.The product of intensive research carried out over the last ten years, this book explores for the first time in a monograph form, results that were only previously available in journal papers.Written in a simple style, with sections and chapters following an easy, natural flow, it will be an invaluable resource for researchers in Operator Theory and Functional Analysis. The reader is assumed to be familiar with the basic notions of linear algebra, functional analysis and complex analysis.

The objective is to understand its symmetries as geometric properties of super Riemann surfaces, which are particular complex super manifolds of dimension 1|1.The first part gives an introduction to the super differential geometry of families of super manifolds.

La théorie des groupes algébriques sur un corps arbitraire est l¿une des branches les plus merveilleuses des mathématiques modernes. Cette monographie porte sur les groupes algébriques semi-simples définis sur un corps k de dimension cohomologique séparable ¿2 et la cohomologie galoisienne d¿iceux. La question ouverte la plus importante est la conjecture II de Serre (1962) qui prédit l¿annulation de la cohomologie galoisienne d¿un groupe semi-simple simplement connexe.Utilisant principalement des techniques de groupes algébriques, on couvre tous les cas connus de la conjecture: les cas classiques (dus à Bayer-Fluckiger and Parimala) ainsi que les avancées sur les cas exceptionnels restants (par exemple de type E8). Ceci s¿applique à la classification des groupes semi-simples. The theory of algebraic groups over arbitrary fields is one of the most beautiful branches of modern mathematics. This monograph deals with semisimple algebraic groups over a general field k of separable cohomological dimension ^ to Bayer-Fluckiger and Parimala), and some perspectives are given on the remaining exceptional cases (e.g., G of type E8). Applications to the classification of semisimple k-groups are presented.

The purpose of this book is to build the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for research on arithmetic geometry in several directions.

This book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations.This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.

The relevance of 2-Segal spaces in the study of Hall and Hecke algebras is discussed.Higher Segal Spaces marks the beginning of a program to systematically study d-Segal spaces in all dimensions d.

This is a primer on a mathematically rigorous renormalisation group theory, presenting mathematical techniques fundamental to renormalisation group analysis such as Gaussian integration, perturbative renormalisation and the stable manifold theorem.

This book presents a new and original method for the solution of boundary value problems in angles for second-order elliptic equations with constant coefficients and arbitrary boundary operators. This method turns out to be applicable to many different areas of mathematical physics, in particular to diffraction problems in angles and to the study of trapped modes on a sloping beach. Giving the reader the opportunity to master the techniques of the modern theory of diffraction, the book introduces methods of distributions, complex Fourier transforms, pseudo-differential operators, Riemann surfaces, automorphic functions, and the Riemann-Hilbert problem.The book will be useful for students, postgraduates and specialists interested in the application of modern mathematics to wave propagation and diffraction problems.

The text continues with Atiyah's question on possible values of (2)-Betti numbers and the relation to Kaplansky's zero divisor conjecture.

This book covers recent advances in several important areas of geometric analysis including extremal eigenvalue problems, mini-max methods in minimal surfaces, CR geometry in dimension three, and the Ricci flow and Ricci limit spaces.

Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions.

This 3rd edition provides an insight into the mathematical crossroads formed by functional analysis (the macroscopic approach), partial differential equations (the mesoscopic approach) and probability (the microscopic approach) via the mathematics needed for the hard parts of Markov processes.

Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. This book presents methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher.

This book presents a series of challenging mathematical problems which arise in the modeling of Non-Newtonian fluid dynamics. It focuses in particular on the mathematical and physical modeling of a variety of contemporary problems, and provides some results. The flow properties of Non-Newtonian fluids differ in many ways from those of Newtonian fluids. Many biological fluids (blood, for instance) exhibit a non-Newtonian behavior, as do many naturally occurring or technologically relevant fluids such as molten polymers, oil, mud, lava, salt solutions, paint, and so on. The term "complex flows" usually refers to those fluids presenting an "internal structure" (fluid mixtures, solutions, multiphase flows, and so on). Modern research on complex flows has increased considerably in recent years due to the many biological and industrial applications.

This book contains three well-written research tutorials that inform the graduate reader about the forefront of current research in multi-agent optimization.

Focusing on arbitrary dimensional schemes, it discusses the important concepts in full generality, complete with proofs, and includes an introduction to the basis of Hironaka's Theory. The core of the book is a complete proof of desingularization of surfaces;

These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors' 2007 Springer monograph "Random Fields and Geometry." While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level.

This self-contained book lays the foundations for a systematic understanding of potential theoretic and uniformization problems on fractal Sierpinski carpets, and proposes a theory based on the latest developments in the field of analysis on metric spaces.

It introduces the category of bornological coarse spaces and the notion of a coarse homology theory, and further constructs the universal coarse homology theory.

This book describes the relation between profinite semigroups and symbolic dynamics. In particular, free profinite semigroups can be seen as the completion of free semigroups with respect to the profinite metric.

This book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups. The presentation is comprehensive, beginning with background information on Hopf algebras, and ending with the classification of admissible representations of the q-deformation of a complex semisimple Lie group. The main components are:- a thorough introduction to quantized universal enveloping algebras over general base fields and generic deformation parameters, including finite dimensional representation theory, the Poincaré-Birkhoff-Witt Theorem, the locally finite part, and the Harish-Chandra homomorphism,- the analytic theory of quantized complex semisimple Lie groups in terms of quantized algebras of functions and their duals,- algebraic representation theory in terms of category O, and- analytic representationtheory of quantized complex semisimple groups. Given its scope, the book will be a valuable resource for both graduate students and researchers in the area of quantum groups.

This monograph is the first comprehensive treatment of multiplicity-free induced representations of finite groups as a generalization of finite Gelfand pairs.

Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied.