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Topological Data Analysis and Beyond
Bastian Rieck · Frederic Chazal · Smita Krishnaswamy · Roland Kwitt · Karthikeyan Natesan Ramamurthy · Yuhei Umeda · Guy Wolf

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The last decade saw an enormous boost in the field of computational
topology: methods and concepts from algebraic and differential topology,
formerly confined to the realm of pure mathematics, have demonstrated
their utility in numerous areas such as computational biology,
personalised medicine, materials science, and time-dependent data
analysis, to name a few.

The newly-emerging domain comprising topology-based techniques is often
referred to as topological data analysis (TDA). Next to their
applications in the aforementioned areas, TDA methods have also proven
to be effective in supporting, enhancing, and augmenting both classical
machine learning and deep learning models.

It is not surprise that there is a steady increase of TDA papers to ML
conferences; in fact, this year's NeurIPS conference has more than 50
papers submitted with the relevant keywords! All of these efforts are
somewhat fragmented, however, and lack a forum for exchanging ideas,
discussing collaborations, and, most importantly, coalescing into
a community.

We believe that it is time to bring together theorists and practitioners
in a creative environment to discuss the goals beyond the
currently-known bounds of TDA. We want to start a conversation between
experts, non-experts, and users of TDA methods to debate the next steps
the field should take. We also want to disseminate methods to a broader
audience and demonstrate how easy the integration of topological
concepts into existing methods can be.