Bøger i Publications of the Scuola Normale Superiore serien

These proceedings contain the contributions of some of the participants in the "e;intensive research period"e; held at the De Giorgi Research Center in Pisa, during the period May-June 2010. The central theme of this research period was the study of configuration spaces from various points of view. This topic originated from the intersection of several classical theories: Braid groups and related topics, configurations of vectors (of great importance in Lie theory and representation theory), arrangements of hyperplanes and of subspaces, combinatorics, singularity theory. Recently, however, configuration spaces have acquired independent interest and indeed the contributions in this volume go far beyond the above subjects, making it attractive to a large audience of mathematicians.

Elementary particle physics is the quadrant of nature whose laws can be written in a few lines with absolute precision and the greatest empirical adequacy.

As explained in the introduction, this represents a useful and important viewpoint in algebraic geometry, especially concerning the theory of algebraic curves and their function fields. of geometrical or topological nature) are often indicated, also to provide motivations and intuition for many results.

The paper contains proofs of most important results in transcendence theory and diophantine analysis, notably Siegel's celebrated theorem on integral points on algebraic curves. Many modern versions of Siegel's proof have appeared, but none seem to faithfully reproduce all features of the original one.

This study provides innovative mathematical models for assessing the eruption probability and associated volcanic hazards, and applies them to the Campi Flegrei caldera in Italy.

In studying this equation, all the necessary material is introduced in the most self-contained way possible, giving precise references to the literature when necessary.The results presented are original, but no particular prerequisite or knowledge of the previous literature is needed to read this text.

These notes are based on the Fermi Lectures delivered at the Scuola Normale Superiore, Pisa, in June 2001.

This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.

This book presents a compact personal biography and a collection of works by Gabriele F. Giuliani's former students and collaborators and a number of personal recollections by friends and colleagues which shed light on the complex, multifaceted personality of a physicist who was also a passionate soccer player and formula Ford pilot.

Contains lecture notes of a series of courses on the regularity theory of partial differential equations and variational problems, held in Pisa and Parma in the years 2009 and 2010.

This book is issued from a conference around resurgent functions in Physics and multiple zetavalues, which was held at the Centro di Ricerca Matematica Ennio de Giorgi in Pisa, on May 18-22, 2015.

We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress of Mathematicians in 1900 in Paris:19th problem: Are the solutions to regular problems in the Calculus of Variations always necessarily analytic?

It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions.

Since 2001 the Scuola Normale Superiore di Pisa has organized the "Colloquio De Giorgi", a series of colloquium talks named after Ennio De Giorgi.

This book presents a series of lectures on three of the best known examples of free discontinuity problems: the Mumford-Shah model for image segmentation, a variational model for the epitaxial growth of thin films, and the sharp interface limit of the Ohta-Kawasaki model for pattern formation in dyblock copolymers.

Since 2001 the Scuola Normale Superiore di Pisa has organized the "Colloquio De Giorgi", a series of colloquium talks named after Ennio De Giorgi.

This book contains papers presented by leading experts at the "Interdisciplinary Workshop on Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (IMRT)" held at the Centro di Ricerca Matematica (CRM) Ennio De Giorgi at Pisa, Italy, from October 15 to 19, 2007.

In the last years a growing attention has been dedicated to many body quantum systems from the point of view of quantum information. This book gives a selection of current research topics in the field of quantum information for many body quantum systems together with open problems.

The contents mainly concern diophantine problems on affine curves, in practice describing the integer solutions of equations in two variables. Starting with linear and quadratic equations, the important connections with Diophantine Approximation are presented and Thue's celebrated results are proved in full detail.

This book deals with some questions related to the boundary problem in complex geometry and CR geometry. It discusses the structure properties of non-compact Levi-flat submanifolds of Cn.

This volume collects the lecture notes of a course on statistical mechanics, held at Scuola Normale Superiore di Pisa for third-to-fifth year students in physics and chemistry.

The main goal of these lectures is to get students acquainted with a glossary of nonlinear physics. The lectures focus on the following arguments: discussion of nonlinear problems in classical physics; description of nonlinear wave steepening and shock wave formation using the Lagrange variables;

This book contains the notes of an international summer school on Analysis in Metric Spaces. Koskela, Upper gradients and Poincare inequalities; Semmes, Derivatives and difference quotients for Lipschitz or Sobolev functions on various spaces; Wheeden, Some weighted Poincare estimates in spaces of homogenous type.

This book is devoted to studying algorithms for the solution of a class of quadratic matrix and vector equations. then, specific numerical methods are presented for the cases most relevant for applications, and new algorithms and theoretical results developed by the author are presented.

The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in  the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.ΓÇï

The courses provide a deep and up to date insight on challenging mathematical problems and their recent developments: infinite-dimensional analysis, minimal surfaces and isoperimetric problems in the Heisenberg group, regularity of sub-Riemannian geodesics and the regularity theory of minimal currents in any dimension and codimension.

Since 2001 the Scuola Normale Superiore di Pisa has organized the "Colloquio De Giorgi", a series of colloquium talks named after Ennio De Giorgi.

In 2008, a school on the theory of optimal transportation and its applications took place in Pisa, with lectures by F. Barthe, W. Gangbo, F. In this book, the notes of the first three lecturers are collected. They provide a deep insight on concentration inequalities, evolution PDEs of Hamiltonian type, geometric and functional inequalities.

The aim of this book is to provide a self-contained introduction and an up-to-date survey on many aspects of the theory of transport equations and ordinary differential equations with non-smooth velocity fields.