Collecting together contributed lectures and mini-courses, this book details the research presented in a special semester titled "Geometric mechanics - variational and stochastic methods" run in the first half of 2015 at the Centre Interfacultaire Bernoulli (CIB) of the Ecole Polytechnique Fédérale de Lausanne. The aim of the semester was to develop a common language needed to handle the wide variety of problems and phenomena occurring in stochastic geometric mechanics. It gathered mathematicians and scientists from several different areas of mathematics (from analysis, probability, numerical analysis and statistics, to algebra, geometry, topology, representation theory, and dynamical systems theory) and also areas of mathematical physics, control theory, robotics, and the life sciences, with the aim of developing the new research area in a concentrated joint effort, both from the theoretical and applied points of view. The lectures were given by leading specialists indifferent areas of mathematics and its applications, building bridges among the various communities involved and working jointly on developing the envisaged new interdisciplinary subject of stochastic geometric mechanics.
Significant, and usually unwelcome, surprises, such as floods, financial crisis, epileptic seizures, or material rupture, are the topics of Extreme Events in Nature and Society. The book, authored by foremost experts in these fields, reveals unifying and distinguishing features of extreme events, including problems of understanding and modelling their origin, spatial and temporal extension, and potential impact. The chapters converge towards the difficult problem of anticipation: forecasting the event and proposing measures to moderate or prevent it. Extreme Events in Nature and Society will interest not only specialists, but also the general reader eager to learn how the multifaceted field of extreme events can be viewed as a coherent whole.
This edited book presents the problems of time and direction from an interdisciplinary point of view, concentrating in particular on the following relations:o Time and physics
o Time, philosophy and psychology
o Time, mathematics and information theoryIt is a unique contribution by philosophers and scientists who are active in mathematics, physics, biology, engineering, information theory and psychology. Questions such as the existence of a Big Bang, the neurobiological basis regarding the coexistence of free will and determinism, intercultural aspects of time, mathematical models of time, psychopathological features of time, and micro reversibility versus macroscopic irreversibility are studied. It also provides a truly interdisciplinary study of the problematic 'arrow of time'.
In recent years it has become increasingly clear that the dynamics of cities can be best captured by looking at them as complex systems governed by many degrees of freedom, interacting on different space and time scales in a non-linear fashion. The evolution of cities is shaped by internal factors, e. g. decisions taken by ins- tutions and individuals, external causes (international economic context) and by social development. The underlying processes can be slow or fast, acting locally or globally. At a different level, both European cities and megacities are magnets for immigrants (e. g. countries, which have major economical and political pr- lems), leading often to phenomena like marginalization or even ghettization and segregation. They are also hotbeds of economic, political and cultural activity, giving rise, among other things, to relocation and conversion of industries, - valuation of land, and development of new services. These phenomena as quali- tive changes, are opposed to purely quantitative growth processes. They are far from being fully understood, nor they are captured in validated and complete - ban models. For most of urban theory hitherto has been based on the assumption of slowly varying spatial and social structures. Only recently, these assumptions have been questioned, giving rise to models employing dissipative dynamics, s- chastic cellular automata and multi-agent models, fractal geometry, and evoluti- ary change models, and to further mathematically oriented approaches.
This book gives its readers a unique opportunity to get acquainted with new aspects of the fruitful interactions between Analysis, Geometry, Quantum Mechanics and Number Theory. The present book contains a number of contributions by specialists in these areas as an homage to the memory of the mathematician Erik Balslev and, at the same time, advancing a fascinating interdisciplinary area still full of potential. Erik Balslev has made original and important contributions to several areas of Mathematics and its applications. He belongs to the founders of complex scaling, one of the most important methods in the mathematical and physical study of eigenvalues and resonances of Schrdinger operators, which has been very essential in advancing the solution of fundamental problems in Quantum Mechanics and related areas. He was also a pioneer in making available and developing spectral methods in the study of important problems in Analytic Number Theory.
