Abstract:

Homology is a widely used tool from Algebraic Topology. It is used to compute the Topological features of a space such as connected components, holes, cavities etc.

Last two decades have seen an increase of applications of tools from Algebraic Topology to problems in Data Analysis. A field that emerged as a result is called Topological Data Analysis. The main tool here is called Persistent Homology, which computes topological features that persist across multiple scales.

My plan for the talk is to give an overview of Homology using Simplicial Complexes and to explain filtrations of Simplicial Complexes. Then I will explain the concept of Persistent Homology using Simplicial Complexes.