الصفحة 1
الصفحة 1
Modern Trends in Pseudo-Differential Operators
The ISAAC Group in Pseudo-diferential Operators (IGPDO) was formed at the Fourth ISAAC Congress held at York University in Toronto in 2003 and the Frst volume entitled Advances in Pseudo-di?erential Operators and devoted to papers focussing on pseudo-di?erential operators and its diverse applications was then initiated and published in Professor Israel Gohberg’s series Operator Theory: - vances and Applications in 2004.The vision is to seek new directionsfor the broadsubjectonpseudo-diferentialoperatorsand the strategy is to devote the Catania Volume not only to papers based on lectures given at the special session on pseudo-diferential operators, but also invited - pers that bear on the themes of IGPDO.
From Geometry to quantum mechanics : In Honor of Hideki Omori
This volume is composed of invited expository articles by well-known mathematicians in differential geometry and mathematical physics that have been arranged in celebration of Hideki Omori's recent retirement from Tokyo University of Science and in honor of his fundamental contributions to these areas.The papers focus on recent trends and future directions in symplectic and Poisson geometry, global analysis, infinite-dimensional Lie group theory, quantizations and noncommutative geometry, as well as applications of partial differential equations and variational methods to geometry.
Ennio De Giorgi : Selected Papers
The book contains a selection of 43 scientific papers by the great mathematician Ennio De Giorgi (1928-1996), which display the broad range of his achievements and his entire intellectual career as a problem solver and as a proponent of deep and ambitious mathematical theories. All papers are written in English and 17 of them appear also in their original Italian version in order to give an impression of De Giorgi’s original style. The editors also provide a short biography of Ennio De Giorgi and a detailed account of his scientific achievements, ranging from his seminal paper on the solution of Hilbert’s 19th problem to the theory of perimeter and minimal surfaces, the theory of G-convergence and the foundations of mathematics.
Matematica generale con il calcolatore
By introducing mathematical objects, it teaches students how to use a computer to perform numerical and symbolic calculations, define a function and calculate its values, plot and explore graphs, and execute simple algorithms. The course is rich in examples, applications, and models, drawn from economics, physics, biology, statistics, and mathematics itself. The analysis of these models constitutes, in a certain sense, the true purpose of the mathematical theory covered. Automatic calculation tools (mathematics software, spreadsheets) are used extensively to explore and illustrate concepts and properties. Mathcad® software, in particular, was used, both as a calculation tool and as a simple yet powerful programming language. Considerable space is devoted to approximation, emphasizing the distinction between numerical and symbolic calculation; to algorithms as a synthesis of the syntactic and semantic aspects of mathematical objects; and to computer simulation, interpreted as a "physical" experiment and a source of conjecture. The ability to use a calculator marks a sort of "democratization" of mathematics: even complex results, which have always required a broad background of knowledge and laborious calculations, are now quickly accessible to anyone who understands the meaning of mathematical objects and knows how to use the syntax.
An Invitation to Morse Theory
This treatment of Morse Theory focuses on applications and is intended for a graduate course on differential or algebraic topology. This is the first textbook to include topics such as Morse-Smale flows, min-max theory, moment maps and equivariant cohomology, and complex Morse theory.
An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem
This book provides an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state of knowledge regarding Pierre Pansu's celebrated 1982 conjecture regarding the sub-Riemannian isoperimetric profile.
A Mathematical Introduction to Conformal Field Theory
The first part of this book gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. In particular, the conformal groups are determined and the appearance of the Virasoro algebra in the context of the quantization of two-dimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. The second part surveys some more advanced topics of conformal field theory, such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface.
