This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23-April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.

This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23-April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.

These lectures give an elementary introduction to the important recent developments of the applications of N=1 supergravity to the construction of unified models of elementary particle interactions. Topics covered include couplings of supergravity with matter, spontaneous symmetry breaking and the super-higgs effect, construction of supergravity unified models, and the phenomenon of SU(2) x U(1) electroweak-symmetry breaking by supergravity. Experimental consequences of N-1 supergravity unified theory, in particular, the possible supersymmetric decays of the W+/- and Z0 bosons, are also discussed. The treatment presented encompasses a broad class of models, both of the tree breaking as well as the radiative breaking of SU(2) x U(1). Rules of tensor calculus and the explicit construction of the Lagrangian of the Supergravity-matter couplings are given in the appendix.