The Legacy of Niels Henrik Abel. The Abel Bicentennial

The core of the book consists of contributions presented at the Abel bicentennial conference held at the University of Oslo, June 3-8, 2002, commemorating the 200th anniversary of Niels Henrik Abel’s birth. The volume does not contain all the contributions of invited speakers at the conference and not all of the contributors attended the conference. The book contains the opening address of King Harald V and 25 papers devoted to various aspects of Abel’s work. However, the reader can also find here papers treating topics that can be considered as mathematics of the next generation. This includes Manin’s paper on applications of non-commutative geometry in Abelian class field theory for real quadratic fields, Fulton’s paper on quantum cohomology of homogeneous varieties, Kassel’s contribution on Hopf-Galois extensions to non-commutative algebras from the point of view of topology, van den Bergh’s paper on non-commutative crepant resolutions of singularities and Chas and Sullivan’s joint paper on closed string operators in topology leading to Lie bialgebras and higher string algebras. The other contributions describe many aspects of Abel’s work as well as parts of number theory, analysis, algebra and geometry having roots in it. The book contains a huge amount of information of a historical and mathematical nature. It can be recommended not only to those working in fields having roots in one of Abel’s versatile contributions to mathematics, but also to anybody who likes to read how ideas can influence future development.

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