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Geometry and Nature
 
Edited by: Hanna Nencka University of Madeira, Madeira, Portugal
Jean-Pierre Bourguignon IHES, Bures-sur-Yvette, France
Geometry and Nature
Softcover ISBN:  978-0-8218-0607-4
Product Code:  CONM/203
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7794-4
Product Code:  CONM/203.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-0607-4
eBook: ISBN:  978-0-8218-7794-4
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
Geometry and Nature
Click above image for expanded view
Geometry and Nature
Edited by: Hanna Nencka University of Madeira, Madeira, Portugal
Jean-Pierre Bourguignon IHES, Bures-sur-Yvette, France
Softcover ISBN:  978-0-8218-0607-4
Product Code:  CONM/203
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7794-4
Product Code:  CONM/203.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-0607-4
eBook ISBN:  978-0-8218-7794-4
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 Details
     
     
    Contemporary Mathematics
    Volume: 2031997; 296 pp
    MSC: 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 one-day 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 self-contained 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
     
     
    • Part I. Clifford Algebras [ MR 1443910 ]
    • A. Trautman — Clifford and the “square root” ideas [ MR 1443911 ]
    • Birger Iversen — Dirac’s algebra and Brauer-Wall 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. Dubois-Violette — Some aspects of noncommutative differential geometry [ MR 1443921 ]
    • D. Kastler, J. Madore and D. Testard — Connections of bimodules in non-commutative geometry [ MR 1443922 ]
    • B. Iochum, D. Kastler and T. Schücker — Riemannian and non-commutative 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 Self-Similar 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 — Chern-Simons vortices [ MR 1443931 ]
    • Marek Szydłowski — The generalized local instability criterion from the geodesic deviation equation [ MR 1443932 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2031997; 296 pp
MSC: 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 one-day 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 self-contained 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.

  • Part I. Clifford Algebras [ MR 1443910 ]
  • A. Trautman — Clifford and the “square root” ideas [ MR 1443911 ]
  • Birger Iversen — Dirac’s algebra and Brauer-Wall 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. Dubois-Violette — Some aspects of noncommutative differential geometry [ MR 1443921 ]
  • D. Kastler, J. Madore and D. Testard — Connections of bimodules in non-commutative geometry [ MR 1443922 ]
  • B. Iochum, D. Kastler and T. Schücker — Riemannian and non-commutative 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 Self-Similar 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 — Chern-Simons vortices [ MR 1443931 ]
  • Marek Szydłowski — The generalized local instability criterion from the geodesic deviation equation [ MR 1443932 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.