«Topology belongs to the stratosphere of human thought! It might conceivable turn out to be of some use in the 24th.»,
Soljenystine, The First Circle.
As great a writer Soljenystine was, he was off 3 centuries with his prediction. Recent advances in computational topology have made this abstract field of mathematics relevant to society by defining new ways of finding structures in complex dataset.
A central problem in today’s society is how to extract meaningful structures from complex datasets.
What are the best examples of the power of persistent homology / topological tools in real life?
What are the big applications?
General introduction, everything will be detailed in the later sections.