  Topological Data Analysis (TDA) is a rigorous framework that borrows
techniques from geometric and algebraic topology, category theory, and
combinatorics in order to study the "shape" of such complex high-dimensional
data. Research in this area has grown significantly over the last several years
bringing a deeply rooted theory to bear on practical applications in areas such
as genomics, natural language processing, medicine, cybersecurity, energy, and
climate change. Within some of these areas, TDA has also been used to augment
AI and ML techniques.
  We believe there is further utility to be gained in this space that can be
facilitated by a workshop bringing together experts (both theorists and
practitioners) and non-experts. Currently there is an active community of pure
mathematicians with research interests in developing and exploring the
theoretical and computational aspects of TDA. Applied mathematicians and other
practitioners are also present in community but do not represent a majority.
This speaks to the primary aim of this workshop which is to grow a wider
community of interest in TDA. By fostering meaningful exchanges between these
groups, from across the government, academia, and industry, we hope to create
new synergies that can only come through building a mutual comprehensive
awareness of the problem and solution spaces.
