Belen Garcia Pascual: Determining homology of an unknown space from a sample

Abstract.

How can we find the shapes and underlying structures of an unknown space? In this talk, we will see results in topological data analysis to reconstruct the topological features of an unknown Euclidean subspace from just a sample of points in the subspace, without reference to the ambient Euclidean space.

We will work with the intrinsic Čech complex formed just from the sample. We will give conditions on the sample and on the unkown subspace, so that the homology of the subspace is given by the persistent homology of the intrinsic Čech complex.

I will also introduce and motivate main concepts in topological data analysis.