Reeb Graphs and Their Measure Theoretic Variants: Theory and Applications

A Reeb graph is a graphical representation of a scalar function on a topological space that encodes the topology of the level sets. Reeb graphs and their variants are popular tools in topological data analysis and visualization. In this talk, I will discuss theoretical advances in studying Reeb graphs and their variants, as well as their applications in data mining and machine learning. In particular, I will discuss novel constructions of Reeb graphs that incorporate the use of a measure, which capture robust topology in data.