You are here

The Legacy of Niels Henrik Abel: The Abel Bicentennial, Oslo, 2002

Olav Arnfinn Laudal and Ragni Piene, editors
Publisher: 
Springer Verlag
Publication Date: 
2004
Number of Pages: 
784
Format: 
Hardcover
Price: 
79.95
ISBN: 
3-540-43826-2
Category: 
Anthology
[Reviewed by
Fernando Q. Gouvêa
, on
01/1/2005
]

What better way to commemorate the bicentennial of Niels Henrik Abel's birth than to bring together a bunch of mathematicians to talk about his work and where it has led? The conference was held in Oslo in June of 2002, and coincided with the launch of the Abel Prize in Mathematics. There is no doubt that it was a grand event.

The book on The Legacy of Niels Henrik Abel is a result of the conference, but it is not your typical proceedings volume. Contributions to the book were solicited before the conference, and there is only partial overlap between the book's content and the talks given at the conference.

Several of the articles in the book are historical and/or biographical. Some, such as Arild Stubhaug's short account of the life of Abel, are mostly on the historical end of the spectrum. Others, such as Steven Kleiman's "What is Abel's Theorem Anyway?" are a blend of mathematics and history, inspecting four theorems that are often called "Abel's Theorem", looking at what Abel actually did, and looking at what came after. Several papers are straight mathematics connected, closely or distantly, to Abel's work. The result is a massive book with a lot of interesting material in it. About half of this material should be accessible to a wide audience; the other half will be of interest mostly to specialists.

With the book comes a CD-ROM containing still more material related to Abel and to the conference. In particular, one can find information on the Centennial Conference held in 1902 (including talks by Sylow and Picard), many pictures, reproductions of stamps, statues, and coins featuring Abel. There is information about the Abel Prize and about honorary doctorates granted at the celebration. There is even an ad for a special edition of Abel's collected works.

It's a delightful package, particularly for those of us who are interested in the history of mathematics and/or in number theory, algebraic geometry, and complex function theory. Just the images on the CD would make me want to have a copy. Given the size of this book and the extras on the CD, this isn't even very expensive; no library should be without a copy.


Fernando Q. Gouvêa is Professor of Mathematics at Colby College; he is the editor of MAA Reviews.

The Legacy of Niels Henrik Abel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
King Harald V
Opening address
The Abel Bicentennial Conference University of Oslo, June 3, 2002 . . . . . 5
Arild Stubhaug
The Life of Niels Henrik Abel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Christian Houzel
The Work of Niels Henrik Abel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Phillip Griffiths
The Legacy of Abel in Algebraic Geometry . . . . . . . . . . . . . . . . . . . . . . . . 179
Daniel Lazard
Solving Quintics by Radicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Birgit Petri and Norbert Schappacher
From Abel to Kronecker: Episodes from 19th Century Algebra . . . . . . . . . 227
Gùunther Frei
On the History of the Artin Reciprocity Law in Abelian Extensions
of Algebraic Number Fields: How Artin was Led to his Reciprocity Law . 267
Aldo Brigaglia, Ciro Ciliberto, Claudio Pedrini
The Italian School of Algebraic Geometry and Abel's Legacy . . . . . . . . . . 295
Fabrizio Catanese
From Abel's Heritage: Transcendental Objects
in Algebraic Geometry and Their Algebraization . . . . . . . . . . . . . . . . . . . . 349
Steven L. Kleiman
What is Abel's Theorem Anyway? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
Torsten Ekedahl
On Abel's Hyperelliptic Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
Mark Green, Phillip Griffiths
Formal Deformation of Chow Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
Herbert Clemens
An Analogue of Abel's Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
Tom Graber, Joe Harris, Barry Mazur, Jason Starr
Arithmetic Questions Related to Rationally Connected Varieties . . . . . . . . 531
Yum-Tong Siu
Hyperbolicity in Complex Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543
G. M. Henkin
Abel-Radon Transform and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 567
Simon Gindikin
Abel Transform and Integral Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585
V. P. Palamodov
Abel's Inverse Problem and Inverse Scattering . . . . . . . . . . . . . . . . . . . . . . 597
Jan-Erik Bjùork
Residues and D-modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
Mikael Passare, August Tsikh
Algebraic Equations and Hypergeometric Series . . . . . . . . . . . . . . . . . . . . . 653
Høakan Hedenmalm
Dirichlet Series and Functional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 673
Yuri I. Manin
Real Multiplication and Noncommutative Geometry . . . . . . . . . . . . . . . . . 685
William Fulton
On the Quantum Cohomology of Homogeneous Varieties . . . . . . . . . . . . . 729
Christian Kassel
Quantum Principal Bundles up to Homotopy Equivalence . . . . . . . . . . . . . 737
Michel van den Bergh
Non-commutative Crepant Resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 749
Moira Chas, Dennis Sullivan
Closed String Operators in Topology Leading to Lie Bialgebras
and Higher String Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 771

Dummy View - NOT TO BE DELETED