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Full Description
This book contains a series of research papers on subjects related to the work of Niels Henrik Abel, written by some of the foremost specialists in their fields.
Some of the authors have been specifically invited to present papers, discussing the influence of Abel in a mathematical-historical context. Others have submitted papers presented at the Abel Bicentennial Conference, Oslo June 3-8, 2002. The idea behind the book has been to produce a text covering a substantial part of the legacy of Abel, as perceived at the beginning of the 21st century.
It is accompanied by a CD-ROM with a large amount of information related to Niels Henrik Abel, such as on the Abel Centennial in 1902 and the Abel Bicentennial Conference in 2002, the launching of the Abel Prize, Abel monuments, and stamps, banknotes, coins etc. issued in honour of Niels Henrik Abel.
Contents
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 Abel's Legacy.- From Abel's Heritage: Transcendental Objects in Algebraic Geometry and Their Algebraization.- What is Abel's Theorem Anyway?.- On Abel's Hyperelliptic Curves.- Formal Deformation of Chow Groups.- An Analogue of Abel's Theorem.- Arithmetic Questions Related to Rationally Connected Varieties.- Hyperbolicity in Complex Geometry.- Abel-Radon Transform and Applications.- Abel Transform and Integral Geometry.- Abel'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.
