Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeperinsights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subjectand closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, i...
Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures, as they appear frequently in almost all natural sciences or technical fields. Although its roots can be traced back to the 18th century (the Buffon needle problem), the modern theory of random sets was founded by D. Kendall and G. Matheron in the early 1970's. Its rapid development was influenced by applications in Spatial Statistics and by its close connections to Integral Geometry. The volume "Stochastic Geometry" contains the lectures given at the CIME summer...
Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures, as they appear frequently in ...
The C.I.M.E. session on Dynamical Systems, held in Cetraro (Italy), June 19-26, 2000, focused on the latest developments in several important areas in dynamical systems, with full development and historical context. The lectures of Chow and Mallet-Paret focus on the area of lattice differential systems, the lectures of Conto and Galleotti treat the classical problem of classification of orbits for two-dimensional autonomous systems with polynomial right sides, the lectures of Nussbaum focus on applications of fixed point theorems to the problem of limiting profiles for the solutions of...
The C.I.M.E. session on Dynamical Systems, held in Cetraro (Italy), June 19-26, 2000, focused on the latest developments in several important areas...
The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. Thus the papers included in the proceedings are surveys and notes on the most important topics of this area of research. They include infinitesimal methods in Hodge theory; algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.
The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make ...
This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro, Italy in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. Coverage includes transport equations for nonsmooth vector fields, viscosity methods for the infinite Laplacian, and geometrical aspects of symmetrization.
This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetr...
Six leading experts lecture on a wide spectrum of recent results on the subject of the title, providing both a solid reference and deep insights on current research activity. Michael Cowling presents a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces. Alain Valette recalls the concept of amenability and shows how it is used in the proof of rigidity results for lattices of semisimple Lie groups. Edward Frenkel describes the geometric Langlands correspondence for complex algebraic curves, concentrating on the...
Six leading experts lecture on a wide spectrum of recent results on the subject of the title, providing both a solid reference and deep insights on...
These lectures 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.
These lectures cover a large spectrum of the subject on the field, from the algebro-geometric point of view, to the symplectic approach, including rec...
In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Some of the classical problems were solved and new classes of minimal surfaces found. Minimal surfaces are now studied from several different viewpoints using methods and techniques from analysis (real and complex), topology and geometry. In this lecture course, Meeks, Ros and Rosenberg, three of the main architects of the modern edifice, present some of the more recent methods and developments of the theory. The topics include moduli, asymptotic geometry...
In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Some of the cla...
Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related...
Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gaug...
The aim of this volume that presents lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex systems in the natural sciences, with a special attention to biology and medicine. Mastering complexity implies sharing different tools requiring much higher level of communication between different mathematical and scientific schools, for solving classes of problems of the same nature. Today more than ever, one of the most important...
The aim of this volume that presents lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of...
