Topology-based methods are of increasing importance in the analysis and
visualization of dataset from a wide variety of scientific domains such
as biology, physics, engineering, and medicine. Current challenges of
topology-based techniques include the management of time-dependent data,
the representation large and complex datasets, the characterization of
noise and uncertainty, the effective integration of numerical methods
with robust combinatorial algorithms, etc. (see also below for a list of
selected issues). While there is an increasing number of high-quality
publications in this field, many fundamental questions remain unsolved.
New focused efforts are needed in a variety of techniques ranging from
the theoretical foundations of topological models, algorithmic issues
related to the representation power of computer-based implementations as
well as their computational efficiency, user interfaces for presentation
of quantitative topological information, and the development of new
techniques for systematic mapping of science problems in topological
constructs that can be solved computationally. In this forum the editors
have brought together the most prominent and best recognized researchers
in the field of topology-based data analysis and visualization for a
joint discussion and scientific exchange of the latest results in the
field. The 2009 workshop in Snowbird, Utah, follows the two successful
workshops in 2005 (Budmerice, Slovakia) and 2007 (Leipzig, Germany).
