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Softcover ISBN:  9780821806074 
Product Code:  CONM/203 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9780821877944 
Product Code:  CONM/203.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821806074 
eBook ISBN:  9780821877944 
Product Code:  CONM/203.B 
List Price:  $255.00 $192.50 
MAA Member Price:  $229.50 $173.25 
AMS Member Price:  $204.00 $154.00 

Book DetailsContemporary MathematicsVolume: 203; 1997; 296 ppMSC: Primary 15; 16; 30; 53; 83;
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.
ReadershipAdvanced graduate students, research mathematicians, mathematical physicists, astrophysicists, cosmologists, and statisticians interested in differential geometry, complex analysis, and algebra.

Table of Contents

Part I. Clifford Algebras [ MR 1443910 ]

A. Trautman — Clifford and the “square root” ideas [ MR 1443911 ]

Birger Iversen — Dirac’s algebra and BrauerWall groups [ MR 1443912 ]

D. Kastler and M. Mebkhout — Linear endomorphisms of Clifford algebras [ MR 1443913 ]

Part II. Riemannian Surfaces [ MR 1443910 ]

I. Kra — Uniformizations of Riemann surfaces: Poincaré theta series, Riemann’s theta function and theta constants [ MR 1443914 ]

William Abikoff — Adapted metrics and Möbius transformations defined over Clifford algebras [ MR 1443915 ]

Part III. Information Geometry [ MR 1443910 ]

S.I. Amari — Information geometry [ MR 1443916 ]

G. Burdet, H. Nencka and M. Perrin — An example of dynamical behaviour of the relative entropy [ MR 1443917 ]

P. Combe and H. Nencka — Information geometry and learning in formal neural networks [ MR 1443918 ]

R. F. Streater — Statistical dynamics and information geometry [ MR 1443919 ]

Part IV. Noncommutative Geometry [ MR 1443910 ]

D. Kastler, J. Madore and T. Masson — On finite differential calculi [ MR 1443920 ]

M. DuboisViolette — Some aspects of noncommutative differential geometry [ MR 1443921 ]

D. Kastler, J. Madore and D. Testard — Connections of bimodules in noncommutative geometry [ MR 1443922 ]

B. Iochum, D. Kastler and T. Schücker — Riemannian and noncommutative geometry in physics [ MR 1443923 ]

Bruno Iochum, Daniel Kastler and Thomas Schücker — Spectral model and fuzzy mass relations [ MR 1443924 ]

Part V. Cosmology and General Relativity [ MR 1443910 ]

M. Demiański — Not so simple universe [ MR 1443925 ]

B. Carter — Extended tensorial curvature analysis for embeddings and foliations [ MR 1443926 ]

T. Papakostas — Spaces admitting a foliation by isotropic hypersurfaces [ MR 1443927 ]

R. Triay — An alternative to inflation [ MR 1443928 ]

Part VI. Symplectic Geometry and SelfSimilar Structures [ MR 1443910 ]

P. Bieliavsky, M. Cahen and S. Gutt — A class of homogeneous symplectic manifolds [ MR 1443929 ]

Jenny Harrison — $r$th order conditionally convergent series of fractal domains [ MR 1443930 ]

Part VII. Field Theory [ MR 1443910 ]

C. Duval and P. A. Horváthy — ChernSimons vortices [ MR 1443931 ]

Marek Szydłowski — The generalized local instability criterion from the geodesic deviation equation [ MR 1443932 ]


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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.
Advanced graduate students, research mathematicians, mathematical physicists, astrophysicists, cosmologists, and statisticians interested in differential geometry, complex analysis, and algebra.

Part I. Clifford Algebras [ MR 1443910 ]

A. Trautman — Clifford and the “square root” ideas [ MR 1443911 ]

Birger Iversen — Dirac’s algebra and BrauerWall groups [ MR 1443912 ]

D. Kastler and M. Mebkhout — Linear endomorphisms of Clifford algebras [ MR 1443913 ]

Part II. Riemannian Surfaces [ MR 1443910 ]

I. Kra — Uniformizations of Riemann surfaces: Poincaré theta series, Riemann’s theta function and theta constants [ MR 1443914 ]

William Abikoff — Adapted metrics and Möbius transformations defined over Clifford algebras [ MR 1443915 ]

Part III. Information Geometry [ MR 1443910 ]

S.I. Amari — Information geometry [ MR 1443916 ]

G. Burdet, H. Nencka and M. Perrin — An example of dynamical behaviour of the relative entropy [ MR 1443917 ]

P. Combe and H. Nencka — Information geometry and learning in formal neural networks [ MR 1443918 ]

R. F. Streater — Statistical dynamics and information geometry [ MR 1443919 ]

Part IV. Noncommutative Geometry [ MR 1443910 ]

D. Kastler, J. Madore and T. Masson — On finite differential calculi [ MR 1443920 ]

M. DuboisViolette — Some aspects of noncommutative differential geometry [ MR 1443921 ]

D. Kastler, J. Madore and D. Testard — Connections of bimodules in noncommutative geometry [ MR 1443922 ]

B. Iochum, D. Kastler and T. Schücker — Riemannian and noncommutative geometry in physics [ MR 1443923 ]

Bruno Iochum, Daniel Kastler and Thomas Schücker — Spectral model and fuzzy mass relations [ MR 1443924 ]

Part V. Cosmology and General Relativity [ MR 1443910 ]

M. Demiański — Not so simple universe [ MR 1443925 ]

B. Carter — Extended tensorial curvature analysis for embeddings and foliations [ MR 1443926 ]

T. Papakostas — Spaces admitting a foliation by isotropic hypersurfaces [ MR 1443927 ]

R. Triay — An alternative to inflation [ MR 1443928 ]

Part VI. Symplectic Geometry and SelfSimilar Structures [ MR 1443910 ]

P. Bieliavsky, M. Cahen and S. Gutt — A class of homogeneous symplectic manifolds [ MR 1443929 ]

Jenny Harrison — $r$th order conditionally convergent series of fractal domains [ MR 1443930 ]

Part VII. Field Theory [ MR 1443910 ]

C. Duval and P. A. Horváthy — ChernSimons vortices [ MR 1443931 ]

Marek Szydłowski — The generalized local instability criterion from the geodesic deviation equation [ MR 1443932 ]