Title | The Legacy of Niels Henrik Abel [electronic resource] : The Abel Bicentennial, Oslo, 2002 / edited by Olav Arnfinn Laudal, Ragni Piene |
---|---|

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004 |

Connect to | http://dx.doi.org/10.1007/978-3-642-18908-1 |

Descript | IX, 784 p. online resource |

SUMMARY

Abel's influence on modern mathematics is substantial. This is seen in many ways, but maybe clearest in the number of mathematical terms containing the adjective Abelian. In algebra, algebraic and complex geometry, analysis, the theory of differential and integral equations, and function theory there are terms like Abelian groups, Abelian varieties, Abelian integrals, Abelian functions. A number of theorems are attributed to Abel. The famous Addition Theorem of Abel, proved in his Paris Mรฉmoire, stands out, even today, as a mathematical landmark. This book, written by some of the foremost specialists in their fields, contains important survey papers on the history of Abel and his work in several fields of mathematics. The purpose of the book is to combine a historical approach to Abel with an overview of his scientific legacy as perceived at the beginning of the 21st century

CONTENT

The Legacy of Niels Henrik Abel -- Opening address The Abel Bicentennial Conference University of Oslo, June 3, 2002 -- The Life of Niels Henrik Abel -- The Work of Niels Henrik Abel -- The Legacy of Abel in Algebraic Geometry -- Solving Quintics by Radicals -- From Abel to Kronecker: Episodes from 19th Century Algebra -- On the History of the Artin Reciprocity Law in Abelian Extensions of Algebraic Number Fields: How Artin was Led to his Reciprocity Law -- The Italian School of Algebraic Geometry and Abelโ{128}{153}s Legacy -- From Abelโ{128}{153}s Heritage: Transcendental Objects in Algebraic Geometry and Their Algebraization -- What is Abelโ{128}{153}s Theorem Anyway? -- On Abelโ{128}{153}s Hyperelliptic Curves -- Formal Deformation of Chow Groups -- An Analogue of Abelโ{128}{153}s Theorem -- Arithmetic Questions Related to Rationally Connected Varieties -- Hyperbolicity in Complex Geometry -- Abel-Radon Transform and Applications -- Abel Transform and Integral Geometry -- Abelโ{128}{153}s Inverse Problem and Inverse Scattering -- Residues and D-modules -- Algebraic Equations and Hypergeometric Series -- Dirichlet Series and Functional Analysis -- Real Multiplication and Noncommutative Geometry -- On the Quantum Cohomology of Homogeneous Varieties -- Quantum Principal Bundles up to Homotopy Equivalence -- Non-commutative Crepant Resolutions -- Closed String Operators in Topology Leading to Lie Bialgebras and Higher String Algebra

Mathematics
Algebraic geometry
Mathematical analysis
Analysis (Mathematics)
Functional analysis
Differential equations
Partial differential equations
History
Mathematics
Algebraic Geometry
Analysis
Functional Analysis
History of Mathematical Sciences
Ordinary Differential Equations
Partial Differential Equations