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Fall 2014 Research Clusters

To participate in a research cluster please apply through the semester program visitors application. Indicate which research cluster you are applying to in the "other comments" section of the application.


Research Cluster: Computational Challenges in Sparse and Redundant Representations (November 3-21, 2014)


Organizers:
Description

Harmonic analysis provides the mathematical backbone for modern signal and image processing. It also constitutes an important part of the foundation several scientific and engineering areas, including communication theory, control science, fluid dynamics, and electromagnetics, that underpin a much broader set of current applications. Although computer implementation of concepts from harmonic analysis is prevalent, relatively little attention is given to computational and numerical aspects of the discipline in its own literature. Further, many of the most capable young mathematicians working in this area have only modest exposure to the roles of such crucial computational considerations as finite data effects; e.g., How much error is introduced by truncating this infinite-series representation of a function in terms of a frame, and where will it be manifested?

On the other hand, new tools and ideas have entered the mainstream of harmonic analysis in recent years that have not yet become established in areas of applied mathematics where numerical and computational issues are routinely treated as integral aspects of problem formulation and methodological development. Among these are tools for non-orthogonal and overcomplete representations in linear spaces and the exploitation of sparsity and related (e.g., low rank) assumptions in inverse problems of various types. This research cluster seeks to bridge this perceived gap by (i) fostering understanding and appreciation of the computational perspective among harmonic analysts and (ii) increasing awareness of emerging mathematical tools and techniques in applied harmonic analysis among computational mathematicians.


  • Ben Adcock
    (Simon Fraser University)
  • Akram Aldroubi
    (Vanderbilt University)
  • Rick Archibald
    (Oak Ridge National Laboratory)
  • Amir Averbuch
    (Tel Aviv University)
  • Radu Balan
    (University of Maryland)
  • Afonso Bandeira
    (Princeton University)
  • Amit Bermanis
    (Tel Aviv University)
  • Ole Christensen
    (Technical University of Denmark)
  • Jacqueline Davis
    (Vanderbilt University)
  • Nira Dyn
    (Tel Aviv University)
  • Milana Gataric
    (University of Cambridge)
  • Anne Gelb
    (Arizona State University)
  • Karlheinz Gröchenig
    (Universität Wien)
  • Philipp Grohs
    (ETH)
  • Daan Huybrechs
    (Katholieke Universiteit Leuven)
  • Jakob Lemvig
    (Technical University of Denmark)
  • Roel Matthysen
    (Katholieke Universiteit Leuven)
  • Dustin Mixon
    (Air Force Institute of Technology)
  • Rodrigo Platte
    (Arizona State University)
  • Jose Luis Romero
    (Universität Wien)
  • Chi-Wang Shu
    (Brown University)
  • Guohui Song
    (Clarkson University)
  • Aditya Viswanathan
    (Michigan State University)
  • Yang Wang
    (Michigan State University)
  • Xiaosheng Zhuang
    (City University of Hong Kong)