Bücher der Reihe Lecture Notes in Mathematics

The book gathers the lectures given at the C.I.M.E. The lectures and the subsequent updating cover a large spectrum of the subject on the field, from the algebro-geometric point of view, to the symplectic approach, including recent developments of string-branes theories and q-hypergeometric functions.

From the contents: Subordinators: Examples and Applications: Foreword.- Elements on subordinators.- Regenerative property.- Asymptotic behaviour of last passage times.- Rates of growth of local time.- Geometric properties of regenerative sets.- Burgers equation with Brownian initial velocity.- Random covering.- L¿ processes.- Occupation times of a linear Brownian motion.- Lectures on Glauber Dynamics for Discrete Spin Models: Introduction.- Gibbs Measures of Lattice Spin Models.- The Glauber Dynamics.- One Phase Region.- Boundary Phase Transitions.- Phase Coexistence.- Glauber Dynamics for the Dilute Ising Model.- Probability on Trees: An Introductory Climb: Preface.- Basic Definitions and a Few Highlights.- Galton-Watson Trees.- General percolation on a connected graph.- The first-Moment method.- Quasi-independent Percolation.- The second Moment Method.- Electrical Networks.- Infinite Networks.- The Method of Random Paths.- Transience of Percolation Clusters.- Subperiodic Trees.- .....

This book on Banach space theory focuses on what have been called three-space problems. It can be considered self-contained, beyond a course in functional analysis and some familiarity with modern Banach space methods.

Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic.

Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter.

Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics. In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence.

Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type.

Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory.

Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. the network's sources and sinks) are known, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it.

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This book is of interest to students as well as experts in the area of real algebraic geometry, quadratic forms, orderings, valuations, lattice ordered groups and rings, and in model theory. The reader needs elementary knowledge of commutative rings, ordered fields and real closed fields and valuations.

The Paris-Princeton Lectures in Financial Mathematics, of which this is the second volume, will, on an annual basis, publish cutting-edge research in self-contained, expository articles from outstanding - established or upcoming!

This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt.

This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.

The main ideas are illustrated in the context of three different physical problems:(i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous.

Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of the various questions raised.

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19-24, 2006

This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems.

Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.

This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jurgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Alvarez Montaner.

Specifically, it covers the stabilization of evolution equations, control of the Liouville equation, control in fluid mechanics, control and numerics for the wave equation, and Carleman estimates for elliptic and parabolic equations with application to control.

Providing a systematic introduction to differential characters as introduced by Cheeger and Simons, this text describes important concepts such as fiber integration, higher dimensional holonomy, transgression, and the product structure in a geometric manner.

Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.

This book deals with various aspects of commutants and reducing subspaces of multiplication operators on the Bergman space, along with relevant von Neumann algebras generated by these operators, which have been the focus of considerable attention from the authors and other experts in recent years.

Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability.

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.