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Fibre spaces --- Congresses --- Colloque de topologie (espaces fibrés) Brussels, 1950

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Most integrable systems owe their origin to problems in geometry and they are best understood in a geometrical context. This is especially true today when the heroic days of KdV-type integrability are over. Problems that can be solved using the inverse scattering transformation have reached the point of diminishing returns. Two major techniques have emerged for dealing with multi-dimensional integrable systems: twistor theory and the d-bar method, both of which form the subject of this book. It is intended to be an introduction, though by no means an elementary one, to current research on integrable systems in the framework of differential geometry and algebraic geometry. This book arose from a seminar, held at the Feza Gursey Institute, to introduce advanced graduate students to this area of research. The articles are all written by leading researchers and are designed to introduce the reader to contemporary research topics.

Fiber spaces (Mathematics). --- Global differential geometry. --- Twistor theory. --- Fiber spaces (Mathematics) --- Fibre spaces (Mathematics) --- Algebraic topology --- Twistors --- Congruences (Geometry) --- Field theory (Physics) --- Space and time --- Geometry, Differential

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Ordered algebraic structures --- Fiber spaces (Mathematics) --- Homotopy theory --- Knot theory --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Knots (Topology) --- Low-dimensional topology --- Deformations, Continuous --- Fibre spaces (Mathematics) --- Algebraic topology --- Homotopy theory. --- Knot theory. --- Noeuds, Théorie des. --- Homotopie. --- Espaces fibrés (mathématiques)

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Affine flag manifolds are infinite dimensional versions of familiar objects such as Graßmann varieties. The book features lecture notes, survey articles, and research notes - based on workshops held in Berlin, Essen, and Madrid - explaining the significance of these and related objects (such as double affine Hecke algebras and affine Springer fibers) in representation theory (e.g., the theory of symmetric polynomials), arithmetic geometry (e.g., the fundamental lemma in the Langlands program), and algebraic geometry (e.g., affine flag manifolds as parameter spaces for principal bundles). Novel aspects of the theory of principal bundles on algebraic varieties are also studied in the book.

Geometry. --- Mathematics. --- Flag manifolds --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Flag manifolds. --- Fiber spaces (Mathematics) --- Fibre spaces (Mathematics) --- Flag varieties (Mathematics) --- Manifolds, Flag --- Varieties, Flag (Mathematics) --- Algebraic geometry. --- Algebraic Geometry. --- Algebraic topology --- Algebraic varieties --- Geometry, algebraic. --- Algebraic geometry

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Homotopy theory

Homotopy theory. --- Algebraic topology. --- Topology --- Deformations, Continuous --- Abelian groups. --- Fiber spaces (Mathematics) --- Spectral sequences (Mathematics) --- Algebra, Homological --- Algebraic topology --- Sequences (Mathematics) --- Spectral theory (Mathematics) --- Fibre spaces (Mathematics) --- Commutative groups --- Group theory