This volume contains the contributions by the participants in the eight of a series workshops in complex analysis, differential geometry and mathematical physics and related areas. Active specialists in mathematical physics contribute to the volume, providing not only significant information for researchers in the area but also interesting mathematics for non-specialists and a broader audience. The contributions treat topics including differential geometry, partial differential equations, integrable systems and mathematical physics.

A discrete model for Kähler magnetic fields on a complex hyperbolic space / T. Adachi -- Integrability condition on the boundary parameters of the asymmetric exclusion process and matrix product ansatz / B. Aneva -- Remarks on the double-complex Laplacian / L. Apostolova -- Generalizations of conjugate connections / O. Calin, H. Matsuzoe, J. Zhang -- Asymptotics of generalized value distribution for Herglotz functions / Y. T. Christodoulides -- Cyclic hyper-scalar systems / S. Dimiev, M. S. Marinov, Z. Zhelev -- Plane curves associated with integrable dynamical systems of the Frenet-Serret type / P. A. Djondjorov, V. M. Vassilev, I. M. Mladenov -- Relativistic strain and electromagnetic photon-like objects / S. Donev, M. Tashkova -- A construction of minimal surfaces in flat tori by swelling / N. Ejiri -- On NLS equations on BD.I symmetric spaces with constant boundary conditions / V. S. Gerdjikov, N. A. Kostov -- Orthogonal almost complex structures on S[symbol] x R[symbol] / H. Hashimoto, M. Ohashi -- Persistence of solutions for some integrable shallow water equations / D. Henry -- Some geometric properties and objects related to Bézier curves / M. J. Hristov -- Heisenberg relations in the general case / B. Z. Iliev -- Poisson structures of equations associated with groups of diffeomorphisms / R. I. Ivanov -- Hyperbolic Gauss maps and parallel surfaces in hyperbolic three-space / M. Kokubu -- On the lax pair for two and three wave interaction system / N. A. Kostov -- Mathematical outlook of fractals and chaos related to simple orthorhombic Ising-Onsager-Zhang lattices / J. Ławrynowicz, S. Marchiafava, M. Nowak-Kepczyk -- A characterization of Clifford minimal hypersurfaces of a sphere in terms of their geodesics / S. Maeda -- On the curvature properties of real time-like hypersurfaces of Kähler manifolds with Norden metric / M. Manev, M. Teofilova -- Some submanifolds of almost contact manifolds with Norden metric / G. Nakova -- A short note on the double-complex Laplace operator / P. Popivanov -- Monogenic, hypermonogenic and holomorphic Cliffordian functions - a survey / I. P. Ramadanoff -- On some classes of exact solutions of eikonal equation / Ł. T. Stepień -- Dirichlet property for tessellations of tiling-type 4 on a plane by congrent pentagons / Y. Takeo, T. Adachi -- Almost complex connections on almost complex manifolds with Norden metric / M. Teofilova -- Pseudo-boson coherent and Fock states / D. A. Trifonov -- New integrable equations of mKdV type / T. I. Valchev -- Integrable dynamical systems of the Frenet-Serret type / V. M. Vassilev, P. A. Djondjorov, I. M. Mladenov

This textbook, first published in 2004, provides an introduction to the major mathematical structures used in physics today.

This book contains the contributions by the participants in the nine of a series of workshops. Throughout the series of workshops, the contributors are consistently aiming at higher achievements of studies of the current topics in complex analysis, differential geometry and mathematical physics and further in any intermediate areas, with expectation of discovery of new research directions. Concerning the present one, it is worthwhile to mention that, in addition to the new developments of the traditional trends, many attractive and pioneering works were presented and their results were contributed to the present volume. The contents of this volume therefore will provide not only significant and useful information for researchers in complex analysis, differential geometry and mathematical physics (including their related areas), but also interesting mathematics for non-specialists and a broad audience. The present volume contains new developments and trends in the studies on constructions of holomorphic Cliffordian functions; the swelling constructions of minimal surfaces with higher genus in flat tori; the spectral properties of soliton equations on symmetric spaces; new types of shallow water waves described by Camassa-Holm type equations, the properties of pseudo-hermitian boson and fermion coherent states; fractals and chaos on orthorhombic lattices, and even an ambitious proposal of a graph model for Kaehler manifolds with Kaehler magnetic fields.

This textbook, pitched at the advanced-undergraduate to beginning-graduate level, focuses on mathematical topics of relevance in contemporary physics that are not usually covered in texts at the same level. Its main purpose is to help students appreciate and take advantage of the modern trend of very productive symbiosis between physics and mathematics. Three major areas are covered: (1) linear operators; (2) group representations and Lie algebra representations; and (3) topology and differential geometry. The features of this work include: an exposition style which is a fusion of those common in the standard physics and mathematics literatures; a level of exposition that varies from quite elementary to moderately advanced, so that the text should be of interest to a wide audience; a strong degree of thematic unity, despite the diversity of the topics covered; and cross references, so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.

For physics students interested in the mathematics they use, and for math students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation strikes a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.

This volume contains the contributions by the participants in the eight of a series workshops in complex analysis, differential geometry and mathematical physics and related areas.Active specialists in mathematical physics contribute to the volume, providing not only significant information for researchers in the area but also interesting mathematics for non-specialists and a broader audience. The contributions treat topics including differential geometry, partial differential equations, integrable systems and mathematical physics.

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.