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Scope of the Abel Symposium, 2006

This symposium will focus on contemporary research involving interaction between computer science, computational science and mathematics. Ever since the early years of computers, applied mathematics has depended heavily upon computational methods. However, in recent years, computation has also been affecting pure mathematics in fundamental ways. Conversely, ideas and methods of pure mathematics are becoming increasingly important within computational and applied mathematics. At the core of computer science is the study of computability and complexity for discrete mathematical structures. Studying the foundations of computational mathematics raises similar questions concerning continuous mathematical structures.

There are several reasons for these developments. The exponential growth of computing power is bringing computational methods into ever new application areas. Equally important is the advance of software and programming languages, which to an increasing degree allows the representation of abstract mathematical structures in program code. Symbolic computing is bringing algorithms from mathematical analysis into the hands of pure and applied mathematicians, and the combination of symbolic and numerical techniques is becoming increasingly important both in computational science and in areas of pure mathematics.

We are witnessing a development where a focus on computability, computing and algorithms is contributing towards a unification of areas of computer science, applied and pure mathematics. The basis for this conference is a belief that these developments will prevail in the 21st century. We will bring together some of the leading international researchers working in these areas, present a snapshot of current state of the art, and raise questions about future research directions.