Higher Structures in Geometry and Physics

This volume arises from a meeting organized at IHP in January 2007 in honor of the 80th birthday of Murray Gerstenhaber and the 70th birthday of Jim Stasheff. The meeting was centered on algebraic deformations and higher homotopies, seminal concepts pioneered by Gerstenhaber and Stasheff in the early 1960s that now are ubiquitous in fundamental areas of mathematics (algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics) and of theoretical physics (quantum field theory, string theory).

Expository articles on seminal concepts from a rich and variety of research fields Written by distinguished researchers and exeptional speakers Discusses fundamental research and new directions for growth Includes supplementary material: sn.pub/extras

Contenu
Topics in Algebraic deformation theory.- Origins and breadth of the theory of higher homotopies.- The deformation philosophy, quantization and noncommutative space-time structures.- Differential geometry of Gerbes and differential forms.- Symplectic connections of Ricci type and star products.- Effective BatalinVilkovisky theories, equivariant configuration spaces and cyclic chains.- Noncommutative calculus and the Gauss-Manin connection.- The Lie algebra perturbation lemma.- Twisting Elements in Homotopy G-algebras.- Homological perturbation theory and homological mirror symmetry.- Categorification of acyclic cluster algebras: an introduction.- Poisson and symplectic functions in Lie algebroid theory.- The diagonal of the Stasheff polytope.- Permutahedra, HKR isomorphism and polydifferential Gerstenhaber-Schack complex.- Applications de la bi-quantification a la théorie de Lie.- Higher homotopy Hopf algebras found: A ten year retrospective