Contemporary Mathematics 1997; 443 pp; softcover Volume: 202 ISBN10: 0821805134 ISBN13: 9780821805138 List Price: US$105 Member Price: US$84 Order Code: CONM/202
 "Operads" are mathematical devices which model many sorts of algebras (such as associative, commutative, Lie, Poisson, alternative, Leibniz, etc., including those defined up to homotopy, such as \(A_{\infty}\)algebras). Since the notion of an operad appeared in the seventies in algebraic topology, there has been a renaissance of this theory due to the discovery of relationships with graph cohomology, Koszul duality, representation theory, combinatorics, cyclic cohomology, moduli spaces, knot theory, and quantum field theory. This renaissance was recognized at a special session "Moduli Spaces, Operads, and Representation Theory" of the AMS meeting in Hartford, CT (March 1995), and at a conference "Opérades et Algèbre Homotopique" held at the Centre International de Rencontres Mathématiques at Luminy, France (MayJune 1995). Both meetings drew a diverse group of researchers. The authors have arranged the contributions so as to emphasize certain themes around which the renaissance of operads took place: homotopy algebra, algebraic topology, polyhedra and combinatorics, and applications to physics. Readership Graduate students, research mathematicians, mathematical physicists, and physicists interested in general algebraic systems. Table of Contents  J. P. May  Definitions: operads, algebras, and modules
 J. Stasheff  The prehistory of operads
 J. P. May  Operads, algebras, and modules
 A. Tonks  Relating the associahedron and the permutohedron
 C. Berger  Combinatorial models for real configuration spaces and \(E_n\)operads
 J. Stasheff  From operads to `physically' inspired theories
 A. V. Gnedbaye  Opérades des algèbres \((k+1)\)aires
 J.M. Oudom  Coproduct and cogroups in the category of graded dual Leibniz algebras
 H.J. Baues, M. Jibladze, and A. Tonks  Cohomology of monoids in monoidal categories
 T. F. Fox and M. Markl  Distributive laws, bialgebras, and cohomology
 D. Balavoine  Deformations of algebras over a quadratic operad
 T. P. Bisson and A. Joyal  \(Q\)rings and the homology of the symmetric groups
 J. P. May  Operadic tensor products and smash products
 T. Kimura, A. A. Voronov, and G. J. Zuckerman  Homotopy Gerstenhaber algebras and topological field theory
 Y.Z. Huang  Intertwining operator algebras, genuszero modular functors, and genuszero conformal field theories
 B. Feigin and F. Malikov  Modular functor and representation theory of \(\widehat {sl_2}\) at a rational level
 J. Morava  Quantum generalized cohomology
 J.L. Brylinski and D. A. McLaughlin  Noncommutative reciprocity laws associated to finite groups
