Books in the Lecture Notes in Mathematics series

This 49th volume offers a good sample of the main streams of current research on probability and stochastic processes, in particular those active in France. This includes articles on latest developments on diffusion processes, large deviations, martingale theory, quasi-stationary distribution, random matrices, and many more.

This monograph develops the Gaussian functional capacity theory with applications to restricting the Gaussian Campanato/Sobolev/BV space.

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 concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Moebius disjointness.

This book introduces and develops new algebraic methods to work with relations, often conceived as Boolean matrices, and applies them to topology.

This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory.

This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa.

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.

The book gives a survey of some recent developments in the theory of bundles on curves arising out of the work of Drinfeld and from insights coming from Theoretical Physics. Drinfeld Shtukas (Lectures by G. Drinfeld modules and Elliptic Sheaves (Lectures by U.

Held during algebraic topology special sessions at the Vietnam Institute for Advanced Studies in Mathematics (VIASM, Hanoi), this set of notes consists of expanded versions of three courses given by G.

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

This book addresses the emerging body of literature on the study of rare events in random graphs and networks.

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.

In this monograph we present a review of a number of recent results on the motion of a classical body immersed in an infinitely extended medium and subjected to the action of an external force.

This book presents the classical theorems about simply connected smooth 4-manifolds: intersection forms and homotopy type, oriented and spin bordism, the index theorem, Wall's diffeomorphisms and h-cobordism, and Rohlin's theorem. There is a new proof of Rohlin's theorem using spin structures.

In addition to its further exploration of the subject of peacocks, introduced in recent Seminaires de Probabilites, this volume continues the series' focus on current research themes in traditional topics such as stochastic calculus, filtrations and random matrices.

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.

Taking the Lasso method as its starting point, this book describes the main ingredients needed to study general loss functions and sparsity-inducing regularizers. Examples include the Lasso and group Lasso methods, and the least squares method with other norm-penalties, such as the nuclear norm.

Providing an elementary introduction to branching random walks, the main focus of these lecture notes is on the asymptotic properties of one-dimensional discrete-time supercritical branching random walks, and in particular, on extreme positions in each generation, as well as the evolution of these positions over time.

Focussing on the mathematics related to the recent proof of ergodicity of the (Weil-Petersson) geodesic flow on a nonpositively curved space whose points are negatively curved metrics on surfaces, this book provides a broad introduction to an important current area of research.

The main goal of this book is to find the constructive content hidden in abstract proofs of concrete theorems in Commutative Algebra, especially in well-known theorems concerning projective modules over polynomial rings (mainly the Quillen-Suslin theorem) and syzygies of multivariate polynomials with coefficients in a valuation ring.Simple and constructive proofs of some results in the theory of projective modules over polynomial rings are also given, and light is cast upon recent progress on the Hermite ring and Gröbner ring conjectures. New conjectures on unimodular completion arising from our constructive approach to the unimodular completion problem are presented.Constructive algebra can be understood as a first preprocessing step for computer algebra that leads to the discovery of general algorithms, even if they are sometimes not efficient. From a logical point of view, the dynamical evaluation gives a constructive substitute for two highly nonconstructive toolsof abstract algebra: the Law of Excluded Middle and Zorn's Lemma. For instance, these tools are required in order to construct the complete prime factorization of an ideal in a Dedekind ring, whereas the dynamical method reveals the computational content of this construction. These lecture notes follow this dynamical philosophy.

These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques.

In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kahler structure. On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kahler manifolds.

With regard to sufficient conditions for (B), we introduce hyperbolic systems with nondegenerate characteristics, which contain strictly hyperbolic systems, and prove that the Cauchy problem for hyperbolic systems with nondegenerate characteristics is well posed for any lower order term.