Multidimensional Interleavings and Applications to Topological Inference

Understand

This work concerns the theoretical foundations of persistence-based topological data analysis.

• We develop theory of topological inference in the multidimensional persistence setting, and directly at the (topological) level of filtrations rather than only at the (algebraic) level of persistent homology modules.
• Our main mathematical objects of study are interleavings.
• These are tools for quantifying the similarity between two multidimensional filtrations or persistence modules.