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.
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.