JournalsowrVol. 1 / No. 1DOI 10.4171/owr/2004/13

Discrepancy Theory and Its Applications

  • Bernard Chazelle

    Princeton University, USA
  • William W.L. Chen

    Macquarie University, Sydney, Australia
  • Anand Srivastav

    Christian-Albrechts-Universität zu Kiel, Germany
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Abstract

The meeting was organized by Bernard Chazelle (Princeton), William Chen (Sydney) and Anand Srivastav (Kiel), and was attended by some twenty participants from over ten countries and three continents. The purpose of the meeting was to encourage and enhance dialogue and collaboration between the theoretical and practical aspects of discrepancy theory. The topics covered included: \begin{enumerate} \item Classical discrepancy theory, including low discrepancy sequences, geometric discrepancy and number theoretical aspects. \item Combinatorial discrepancy theory, including coloring of hypergraphs and arithmetic structures. \item Algorithms and complexity, including relations of discrepancy theory to derandomization of probabilistic algorithms and pseudorandomness, complexity classes, data structures in computational geometry and applications in combinatorial optimization. \item Numerical integration in high dimension and its complexity. \end{enumerate} Nineteen talks were presented, including a few of a survey nature as well as others that concentrated on specific recent results. These talks demonstrated the diversity on all four areas and their inter-relationships, as well as the vitality of these areas of research. The organizers and participants would like to take this opportunity to thank again the ``Mathematisches Forschungsinstitut Oberwolfach'' for having provided a comfortable and inspiring environment for the meeting and the scientific work. The pleasant atmosphere and superb facilities contributed to the overall success of the meeting. We include the abstracts of all the talks in alphabetical order of the speakers.