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.

The book provides a non-perturbative approach to the symmetry breaking in the standard model, in this way avoiding the critical issues which affect the standard presentations.

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.

The goal of this book is to be an accessible guide for undergraduate and graduate students to the new field of data-driven biology. Next-generation sequencing technologies have put genome-scale analysis of gene expression into the standard toolbox of experimental biologists. Yet, biological interpretation of high-dimensional data is made difficult by the lack of a common language between experimental and data scientists. By combining theory with practical examples of how specific tools were used to obtain novel insights in biology, particularly in the neurosciences, the book intends to teach students how to design, analyse, and extract biological knowledge from transcriptome sequencing experiments.Undergraduate and graduate students in biomedical and quantitative sciences will benefit from this text as well as academics untrained in the subject.

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.

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.

We study the existence and regularity of optimal domains for functionals depending on the spectrum of the Dirichlet Laplacian or of more general Schroedinger operators.

These lecture notes contain the main topics presented in a series of lectures given at the Scuola Normale di Pisa in the academic years 1998-1999-2000. In the second part, the tools developed are applied to an extensive discussion of selected problems offered by the stellar dynamics of collisionless systems of stars.

These are the written notes of Fermi's Lectures supported by the Accademia Nazionale dei Lincei and given at the Scuola Normale Superiore of Pisa during March-April 1973. Eigenfunctions which correspond to positive eigenvalues are shown to decay rapidly.

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.

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

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.

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 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.

Defining and computing a greatest common divisor of two polynomials with inexact coefficients is a classical problem in symbolic-numeric computation.

Presents the proceedings of a one-week international conference centered on asymptotic analysis and its applications that contain major contributions dealing with: mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis, local dynamics: parabolic systems, and small denominator questions.

While logic lends its methods, techniques and ideas to the investigation of rationality, the practical problems which arise in modelling rational behaviour, especially in the social sciences, motivate logicians to develop more refined logical formalisms.

Presents the proceedings of a one-week international conference centered on asymptotic analysis and its applications. This book contains contributions dealing with mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis, and, local dynamics: parabolic systems, small denominator questions.

If we restrict to minimal algebraic surfaces of general type the above question can be interpreted in terms of properties of the moduli space of surfaces of general type.

The aim of this thesis is to give a complete exposition of the main topological and ergodic properties of the expanding maps and provide some new results about their periodic points sets.

The theory of elliptic complexes of linear partial differential operators is closely interwoven with complex analysis. In this dissertation I apply Green's integrals to the Cauchy problem for elliptic systems and to the question of the validity of the Poincare lemma for elliptic differential complexes.

The present article is based on the Fermi Lectures I gave in May, 1985, at Scuola Normale Superiore, Pisa, in which I discussed various methods for solving the Cauchy problem for abstract nonlinear differential equations of evolution type.

This volume collects some contributed papers by the participants to the workshop "Singularities in nonlinear evolution phenomena and applications", which was held at the Centro di Ricerca Matematica E.

The book is devoted to study the relationships between Stochastic Partial Differential Equations and the associated Kolmogorov operator in spaces of continuous functions.

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.

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 volume presents an introductory course on differential stochastic equations and Malliavin calculus. The first part is devoted to the Gaussian measure in a separable Hilbert space, the Malliavin derivative, the construction of the Brownian motion and Ito's formula. The third part provides an introduction to the Malliavin calculus.

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.