Abstract:

In this talk I will give an introduction of Topological Data Analysis, or more precisely, to one of its main tools: Persistent Homology. The idea behind Persistent Homology is to study the changes on the homology groups of a sequence of nested simplicial complexes. The theory of persistence started around 2005 and has since developed very solid foundations. In the talk I plan to cover some of these, while discussing with you why those where necessary or relevant to the theory. After that, we will relate these pretty much theoretical tools to data problems, and discuss why persistence might be useful in other contexts such as biology of medicine.

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