This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently.
This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include Hopf algebras underlying renormalization schemes in quantum field theory, noncommutative geometry with applications to index theory on one hand and the study of aperiodic solids on the other, geometry and topology of low dimensional manifolds with applications to topological field theory, Chern-Simons supergravity and the anti de Sitter/conformal field theory correspondence. It comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by supergravity and string theory, complemented by some short communications by young participants of the school.
Both mathematics and mathematical physics have many active areas of research where the interplay between geometry and quantum field theory has proved extremely fruitful. Duality, gauge field theory, geometric quantization, SeibergOCoWitten theory, spectral properties and families of Dirac operators, and the geometry of loop groups offer some striking recent examples of modern topics which stand on the borderline between geometry and analysis on the one hand and quantum field theory on the other, where the physicist''s and the mathematician''s perspective complement each other, leading to new mathematical and physical concepts and results. This volume introduces the reader to some basic mathematical and physical tools and methods required to follow the recent developments in some active areas of mathematical physics, including duality, gauge field theory, geometric quantization, Seiberg-Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups. It comprises seven self-contained lectures, which should progressively give the reader a precise idea of some of the techniques used in these areas, as well as a few short communications presented by young participants at the school. Contents: Lectures: Introduction to Differentiable Manifolds and Symplectic Geometry (T Wurzbacher); Spectral Properties of the Dirac Operator and Geometrical Structures (O Hijazi); Quantum Theory of Fermion Systems: Topics Between Physics and Mathematics (E Langmann); Heat Equation and Spectral Geometry. Introduction for Beginners (K Wojciechowski); Renormalized Traces as a Geometric Tool (S Paycha); Concepts in Gauge Theory Leading to Electric-Magnetic Duality (T S Tsun); An Introduction to Seiberg-Witten Theory (H Ocampo); Short Communications: Remarks on Duality, Analytical Torsion and Gaussian Integration in Antisymmetric Field Theories (A Cardona); Multiplicative Anomaly for the e-Regularized Determinant (C Ducourtioux); On Cohomogeneity One Riemannian Manifolds (S M B Kashani); A Differentiable Calculus on the Space of Loops and Connections (M Reiris); Quantum Hall Conductivity and Topological Invariants (A Reyes); Determinant of the Dirac Operator Over the Interval [0, ] (F Torres-Ardila). Readership: Mathematicians and physicists.
Written over a seven-year period to Charles V of Spain, Hernan Cortes's letters provide a narrative account of the conquest of Mexico from the founding of the coastal town of Veracruz until Cortes's journey to Honduras in 1525. The two introductions set the letters in context.
That Borges is one of the key figures in 20th-century literature is beyond debate. The reasons behind this claim, however, are a matter of contention. In Latin America he is read as someone who reorganized the canon, questioned literary hierarchies, and redefined the role of marginal literatures. On the other hand, in the rest of the world, most readers (and dictionaries) tend to identify the adjective "Borgesian" with intricate metaphysical puzzles and labyrinthine speculations of universal reach, completely detached from particular traditions. One reading is context-saturated, while the other is context-deprived. Oddly enough, these "institutional" and "transcendental" approaches have not been pitched against each other in a critical way. Borges, between History and Eternity brings these perspectives together by considering key aspects of Borges's work-the reciprocal determinations of politics, philosophy and literature; the simultaneously confining and emancipating nature of language; and the incipient program for a literature of the Americas.
The Unfinished Song of Francisco Urondo: When Poetry is Not Enough is a comprehensive, well-written, documented, and carefully developed study of the literary work and life of Francisco Urondo, an Argentine poet, intellectual, activist, cultural promoter, revolutionary, and clandestine guerilla member who died in 1976 fighting for a cause in which he believed, against the oppressive Argentine Military Junta. This methodical but never mechanistic work shows how life events, cultural milieu, political movements, and world circumstances interacted and impacted Urondo’s temperament to produce his poetic voice, his prose, and his theatrical works. By studying the man, we get closer to his poetry. With his poetry, the author makes a compelling case for understanding the man. Francisco Urondo’s life, work, and praxis were varied, agonizing at times, and always marked by imperatives. This book fills a significant lacuna in the scholarship on the work of this worthy, yet neglected and under-studied, writer. Readers of this book will come away with not only a deepened understanding of the man and his writings but also of a key period in recent Argentine political, social, and intellectual history.
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