Contemporary Mathematics 1997; 296 pp; softcover Volume: 203 ISBN10: 0821806076 ISBN13: 9780821806074 List Price: US$79 Member Price: US$63.20 Order Code: CONM/203
 This volume is the outgrowth of a conference devoted to William K. Clifford entitled, "New Trends in Geometrical and Topological Methods", which was held at the University of Madeira in July and August 1995. The aim of the conference was to bring together active workers in fields linked to Clifford's work and to foster the exchange of ideas between mathematicians and theoretical physicists. Divided into 6 oneday sessions, each session was devoted to a specific aspect of Clifford's work. This volume is an attempt to bring the Clifford legacy in a new perspective to a larger community of mathematicians and physicists. New concepts, ideas, and results stemming from Clifford's work are discussed. Each article in the book is a selfcontained paper that was presented at or submitted to the conference. Readership Advanced graduate students, research mathematicians, mathematical physicists, astrophysicists, cosmologists, and statisticians interested in differential geometry, complex analysis, and algebra. Table of Contents  H. Nencka and J.P. Bourguignon  W. K. Clifford as a geometer
Part I. Clifford Algebras  A. Trautman  Clifford and the `square root' ideas
 B. Iversen  Dirac's algebra and BrauerWall groups
 D. Kastler and M. Mebkhout  Linear endomorphisms of Clifford algebras
Part II. Riemannian Surfaces  I. Kra  Uniformizations of Riemann surfaces: Poincaré theta series, Riemann's theta function and theta constants
 W. Abikoff  Adapted metrics and Möbius transformations defined over Clifford algebras
Part III. Information Geometry  S.I. Amari  Information geometry
 G. Burdet, H. Nencka, and M. Perrin  An example of dynamical behaviour of the relative entropy
 P. Combe and H. Nencka  Information geometry and learning in formal neural networks
 R. F. Streater  Statistical dynamics and information geometry
Part IV. Noncommutative Geometry  D. Kastler, J. Madore, and T. Masson  On finite differential calculi
 M. DuboisViolette  Some aspects of noncommutative differential geometry
 D. Kastler, J. Madore, and D. Testard  Connections of bimodules in noncommutative geometry
 B. Iochum, D. Kastler, and T. Schücker  Riemannian and noncommutative geometry in physics
 B. Iochum, D. Kastler, and T. Schücker  Spectral model and fuzzy mass relations
Part V. Cosmology and General Relativity  M. Demiański  Not so simple universe
 B. Carter  Extended tensorial curvature analysis for embeddings and foliations
 T. Papakostas  Spaces admitting a foliation by isotropic hypersurfaces
 R. Triay  An alternative to inflation
Part VI. Symplectic Geometry and SelfSimilar Structures  P. Bieliavsky, M. Cahen, and S. Gutt  A class of homogeneous symplectic manifolds
 J. Harrison  \(r^{th}\) order conditionally convergent series of fractal domains
Part VII. Field Theory  C. Duval and P. A. Horváthy  ChernSimons vortices
 M. Szydłowski  The generalized local instability criterion from the geodesic deviation equation
