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Modern geometry - methods and applications : part I : the geometry of surfaces, transformation groups, and fields / par Dubrovin, B.A. Publication : [S.l.] : Springer, 1991 . 492 p. ; , This is the first volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This material is explained in as simple and concrete a language as possible, in a terminology acceptable to physicists. The text for the second edition has been substantially revised. 24 cm. Date : 1991 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Nilpotent lie algebras / par Goze,, M. Publication : [S.l.] : Springer, 1996 . 352 p. ; , This volume is devoted to the theory of nilpotent Lie algebras and their applications. Nilpotent Lie algebras have played an important role over the last years both in the domain of algebra, considering its role in the classification problems of Lie algebras, and in the domain of differential geometry. Among the topics discussed here are the following: cohomology theory of Lie algebras, deformations and contractions, the algebraic variety of the laws of Lie algebras, the variety of nilpotent laws, and characteristically nilpotent Lie algebras in nilmanifolds. Audience: This book is intended for graduate students specialising in algebra, differential geometry and in theoretical physics and for researchers in mathematics and in theoretical physics. 25 cm. Date : 1996 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Noncommutative geometry, quantum fields and motives par Connes, Alain Publication : [S.l.] American Mathematical Society 2008 . 785 p. , The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adele class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function. 27 cm. Date : 2008 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Noncommutative spacetimes : symmetries in noncommutative geometry and field theory par Aschieri, Paolo. Publication : [S.l.] Springer 2009 . 213 p. , There are many approaches to noncommutative geometry and to its use in physics. This volume addresses the subject by combining the deformation quantization approach, based on the notion of star-product, and the deformed quantum symmetries methods, based on the theory of quantum groups. The aim of this work is to give an introduction to this topic and to prepare the reader to enter the research field quickly. The order of the chapters is "physics first": the mathematics follows from the physical motivations (e.g. gauge field theories) in order to strengthen the physical intuition. The new mathematical tools, in turn, are used to explore further physical insights. A last chapter has been added to briefly trace Julius Wess' (1934-2007) seminal work in the field. 25 cm. Date : 2009 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Nonlinear dynamical control systems / par Nijmeijer,, H. Publication : New York : Springer, 1996 . xiii, 467 p. : 25 cm. Date : 1996 Disponibilité : Exemplaires disponibles: La bibliothèque des sciences de l'ingénieur (1),

P-adic deterministic and random dynamics / par Khrennikov,, Andrei Y. Publication : [S.l.] : Springer, 2004 . 270 p. ; , This is the first monograph in the theory of p-adic (and more general non-Archimedean) dynamical systems. The theory of such systems is a new intensively developing discipline on the boundary between the theory of dynamical systems, theoretical physics, number theory, algebraic geometry and non-Archimedean analysis. Investigations on p-adic dynamical systems are motivated by physical applications (p-adic string theory, p-adic quantum mechanics and field theory, spin glasses) as well as natural inclination of mathematicians to generalize any theory as much as possible (e.g., to consider dynamics not only in the fields of real and complex numbers, but also in the fields of p-adic numbers). The main part of the book is devoted to discrete dynamical systems: cyclic behavior (especially when p goes to infinity), ergodicity, fuzzy cycles, dynamics in algebraic extensions, conjugate maps, small denominators. There are also studied p-adic random dynamical system, especially Markovian behavior (depending on p). In 1997 one of the authors proposed to apply p-adic dynamical systems for modeling of cognitive processes. In applications to cognitive science the crucial role is played not by the algebraic structure of fields of p-adic numbers, but by their tree-like hierarchical structures. In this book there is presented a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. There are also studied p-adic neural network and their applications to cognitive sciences: learning algorithms, memory recalling. Finally, there are considered wavelets on general ultrametric spaces, developed corresponding calculus of pseudo-differential operators and considered cognitive applications. Audience: This book will be of interest to mathematicians working in the theory of dynamical systems, number theory, algebraic geometry, non-Archimedean analysis as well as general functional analysis, theory of pseudo-differential operators; physicists working in string theory, quantum mechanics, field theory, spin glasses; psychologists and other scientists working in cognitive sciences and even mathematically oriented philosophers. 25 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Pfaffian systems, K-symplectic systems / par Awane, A. Publication : [S.l.] : Springer, 2000 . 260 p. ; , The geometrical view of mechanics is based on the study of certain exterior systems, the most classical of which are Pfaffian systems. In this book, we present the classification theorems (Frobenius, Darboux) and the local classification of Pfaffian systems of five variables, following Cartan. We also present a new class of exterior systems, called k-symplectic systems, generalizing the notion of symplectic form. These systems permit us to write in the language of exterior forms the equations proposed by Nambu for a model of statistical mechanics. Audience: This book is aimed at graduate students and at research workers in the field of mathematics, differential geometry, statistical mechanics, mathematics of physics and Lie algebras. 25 cm. Date : 2000 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Poisson structures and their normal forms par Dufour, Jean-Paul. Publication : Basel ; Boston Birkhauser 2005 . 321 p. , The aim of this book is twofold. On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books. 24 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Positivity in algebraic geometry I : classical setting : line bundles and linear series / par Lazarsfeld, R. K. Publication : [S.l.] : Springer, 2004 . 387 p. ; , This two volume work on. 24 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Positivity in algebraic geometry ii : positivity for vector bundles, and multiplier ideals / par Lazarsfeld, R. K. Publication : [S.l.] : Springer, 2004 . 385 p. ; , This two volume work on. 23 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Raisonnement et stratégies de preuve dans l'enseignement des mathématiques par Richard, Philippe R. Publication : Bern P. Lang 2004 . xii, 324 p. 21 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Random fields and geometry par Adler, Robert J. Publication : New York Springer 2007 . xvii, 448 pages 24 cm. Date : 2007 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Random matrices, frobenius eigenvalues, and monodromy par Katz, Nicholas M. Publication : [S.l.] American Mathematical Society 1999 . 419 p. , The main topic of this book is the deep relation between the spacings between zeros of zeta and $L$-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and $L$-functions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinity and related techniques from orthogonal polynomials and Fredholm determinants. 26 cm. Date : 1999 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Reconstructive integral geometry / par Palamodov,, V. P. Publication : Boston : BirkhŁauser Verlag, 2004 . ix, 164 p. : 24 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Research problems in discrete geometry par Brass, Peter Publication : New York Springer 2005 . xii, 499 pages 24 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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