Books in the Lecture Notes in Mathematics series

Written by leading experts in an emerging field, this book offers a unique view of the theory of stochastic partial differential equations, with lectures on the stationary KPZ equation, fully nonlinear SPDEs, and random data wave equations.

This volume provides a unified and accessible account of recent developments regarding the real homotopy type of configuration spaces of manifolds.  Configuration spaces consist of collections of pairwise distinct points in a given manifold, the study of which is a classical topic in algebraic topology. One of this theory's most important questions concerns homotopy invariance: if a manifold can be continuously deformed into another one, then can the configuration spaces of the first manifold be continuously deformed into the configuration spaces of the second? This conjecture remains open for simply connected closed manifolds. Here, it is proved in characteristic zero (i.e. restricted to algebrotopological invariants with real coefficients), using ideas from the theory of operads. A generalization to manifolds with boundary is then considered. Based on the work of Campos, Ducoulombier, Lambrechts, Willwacher, and the author, the book covers a vast array of topics, including rational homotopy theory, compactifications, PA forms, propagators, Kontsevich integrals, and graph complexes, and will be of interest to a wide audience.

The author further explores recent trends in the application of operad theory to wiring diagrams and related structures, including finite presentations for the propagator algebra, the algebra of discrete systems, the algebra of open dynamical systems, and the relational algebra.

This book is unique in its attempt to give an overview of dispersal studies across different spatial scales, such as the scale of individual movement, the population scale and the scale of communities and ecosystems.

This volume synthesizes theoretical and practical aspects of both the mathematical and life science viewpoints needed for modeling of the cardiovascular-respiratory system specifically and physiological systems generally.

This volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.

Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice.

Each year young mathematicians congregate in Saint Flour, France, and listen to extended lecture courses on new topics in Probability Theory. This title features notes, representing a course given by Terry Lyons in 2004, that provide an account of the key results forming the foundation of the theory of rough paths.

Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context. Algebras of Iwahori-Hecke type are one of the tools and were, probably, first considered in the context of representation theory of finite groups of Lie type.

This open access book focuses on the interplay between random walks on planar maps and Koebe's circle packing theorem.

Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini.

Studying the fine properties of solutions to Stochastic (Partial) Differential Equations with reflection at a boundary, this book begins with a discussion of classical one-dimensional diffusions as the reflecting Brownian motion, devoting a chapter to Bessel processes, and moves on to function-valued solutions to SPDEs.

This volumebrings together four lecture courses on modern aspects of water waves. Thelectures provide a useful source for those who want to begin to investigate howmathematics can be used to improve our understanding of water wave phenomena.

Providing an introduction to isogeometric methods with a focus on their mathematical foundations, this book is composed of four chapters, each devoted to a topic of special interests for isogeometric methods and their theoretical understanding.

Pluripotential theory is a very powerful tool in geometry, complex analysis and dynamics. This CIME course focused on complex Monge-Ampere equations, applications of pluripotential theory to Kahler geometry and algebraic geometry and to holomorphic dynamics.

Presenting a range of substantive applied problems within Bayesian Statistics along with their Bayesian solutions, this book arises from a research program at CIRM in France in the second semester of 2018, which supported Kerrie Mengersen as a visiting Jean-Morlet Chair and Pierre Pudlo as the local Research Professor.

This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schloemilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions.

The central theme of this reference book is the metric geometry of complex analysis in several variables.

Collecting together the lecture notes of the CIME Summer School held in Cetraro in July 2018, the aim of the book is to introduce a vast range of techniques which are useful in the investigation of complex manifolds.

This book sets out an account of the tools which Frobenius used to discover representation theory for nonabelian groups and describes its modern applications.

The main goal of this book is to provide an overview of the state of the art in the mathematical modeling of complex fluids, with particular emphasis on its thermodynamical aspects.

This three-chapter volume concerns the distributions of certain functionals of Levy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal distributions in terms of mappings of certain Levy processes via stochastic integration.

These lecture notes provide an introduction to the applications of Brownian motion to analysis and more generally, connections between Brownian motion and analysis.

Presenting a selection of topics in the area of nonlocal and nonlinear diffusions, this book places a particular emphasis on new emerging subjects such as nonlocal operators in stationary and evolutionary problems and their applications, swarming models and applications to biology and mathematical physics, and nonlocal variational problems.

Focusing on special matrices and matrices which are in some sense `near' to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra.