Abstract: 

As the amount of data collected has increased in recent years, new methods for understanding data have been sought. One such method, Topological Data Analysis, or TDA, studies data and draws conclusions using the shape of the data set. In this talk, I will briefly walk through the TDA pipeline, before shifting the focus to the stability of multiparameter persistence homology, a measure of the similarity of results after data has been perturbed. In this talk, I will specifically be considering the p-Presentation Distance as a distance on multiparameter persistence modules and its stability. Having introduced the necessary definitions and results, I will conclude by proving that under certain conditions, the p-Presentation Distance is p-stable on finitely presented bipersistence modules.