Bøger i Publications of the Scuola Normale Superiore serien

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 book describes the searches that lead to the discovery of a Higgs boson performed at CMS, one of the two main experiments at the CERN LHC. After an overview of the theory and of the CMS experiment, all search channels are described, with emphasis on the ones with the best sensitivity.

These volumes collect the lecture notes of the course "An introduction to computational physics" held in the academic year 2000/01 for students of the University of Pisa and Scuola Normale Superiore at the level of the last two-year undergraduates in physics and chemistry.

These volumes collect the lecture notes of the course "An introduction to computational physics" held in the academic year 2000/01 for students of the University of Pisa and Scuola Normale Superiore at the level of the last two-year undergraduates in physics and chemistry.

Features contributions in the following different fields: Holomorphic dynamics and foliations, Hamiltonian dynamics, Small divisor problems, Celestial mechanics, Ergodic theory and randomly perturbed systems, Periodic orbits and zeta functions, Topology and dynamics, and Partially hyperbolic and non-uniformly hyperbolic systems.

The book is devoted to the study of submanifolds in the setting of Carnot groups equipped with a sub-Riemannian structure; Intrinsically regular hypersurfaces in the Heisenberg group are extensively studied: suitable notions of graphs are introduced, together with area formulae leading to the analysis of Plateau and Bernstein type problems.

Includes contributions in such fields as Holomorphic dynamics and foliations, Hamiltonian dynamics, Small divisor problems, Celestial mechanics, Ergodic theory and randomly perturbed systems, Periodic orbits and zeta functions, Topology and dynamics, and Partially hyperbolic and non-uniformly hyperbolic systems.

Topics include, but are not limited to: Algebraic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial optimization, designs and configurations, enumerative combinatorics, extremal combinatorics, ordered sets, random methods, topological combinatorics.

This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions.

The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces.

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?

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

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

This book introduces some methods for the determination of the three-dimensional geometry of molecules in solution and the occurrence of dynamical processes (interaction with the solvent, rearrangements in the molecular geometry, interactions with other molecules) in several ytterbium complexes.

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.

This course will develop the parallel between the geometry of a compact, oriented differentiable manifold M endowed with a Riemannian metric and the geometry of a compact (oriented) complex manifold M with a Riemannian metric compatible with the complex structure. Such a metric is called a Kahler metric for M.

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;

The scope of the short series of lectures was to extend on general grounds, also to mathematicians, the phenomenon of Spontaneous Symmetry Breaking (SSB), a mechanism which seems at the basis of the recent developments in theoretical physics (from statistical mechanics to many-body theory and to elementary particle theory).

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.

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.

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.

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 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.

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

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.

We give a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case. We further analyze the relation between differential calculus and quantum Lie algebra of left (right) invariant vectorfields.

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.

In that case, the dynamic programming equation is a nonlinear partial differential equation of second order elliptic or parabolic type. From the viewpoint of nonlinear evolution equations, the interest is in whether one can find some stochastic control problem for which the given evolution equation is the dynamic programming equation.

Prepared for the Special Research Semester on Financial Markets, which was held in Pisa, from April 29 to July 15, 2002, this title covers topics such as the Hamilton-Jacobi-Bellman approach to stochastic control problems, with applications to finance.

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.