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The unifying theme of this collection of papers by the very creative Russian mathematician I. M. Gelfand and his co-workers is the representation theory of groups and lattices. Two of the papers were inspired by application to theoretical physics; the others are pure mathematics though all the papers will interest mathematicians at quite opposite ends of the subject. Dr. G. Segal and Professor C-M. Ringel have written introductions to the papers which explain the background, put them in perspective and make them accessible to those with no specialist knowledge in the area.

Representations of groups. --- Representations of algebras. --- Algebra --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Representations of groups --- Representations of algebras

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A tribute to the vision and legacy of Israel Moiseevich Gelfand, the invited papers in this volume reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory. Written by leading mathematicians, the text is broadly divided into two sections: the first is devoted to developments at the intersection of geometry and physics, and the second to representation theory and algebraic geometry. Topics include conformal field theory, K-theory, noncommutative geometry, gauge theory, representations of infinite-dimensional Lie algebras, and various aspects of the Langlands program. Graduate students and researchers will benefit from and find inspiration in this broad and unique work, which brings together fundamental results in a number of disciplines and highlights the rewards of an interdisciplinary approach to mathematics and physics. Contributors: M. Atiyah; A. Braverman; H. Brezis; T. Coates; A. Connes; S. Debacker; V. Drinfeld; L.D. Faddeev; M. Finkelberg; D. Gaitsgory; I.M. Gelfand; A. Givental; D. Kazhdan; M. Kontsevich; B. Kostant; C-H. Liu; K. Liu; G. Lusztig; D. McDuff; M. Movshev; N.A. Nekrasov; A. Okounkov; N. Reshetikhin; A. Schwarz; Y. Soibelman; C. Vafa; A.M. Vershik; N. Wallach; and S-T. Yau.

Mathematics --- Algebra. --- Mathematical analysis --- Math --- Science --- Geometry. --- Mathematical physics. --- Topological Groups. --- Geometry, algebraic. --- K-theory. --- Group theory. --- Mathematical Methods in Physics. --- Topological Groups, Lie Groups. --- Algebraic Geometry. --- K-Theory. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Algebraic topology --- Homology theory --- Algebraic geometry --- Geometry --- Groups, Topological --- Continuous groups --- Physical mathematics --- Physics --- Euclid's Elements --- Physics. --- Topological groups. --- Lie groups. --- Algebraic geometry. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics