Explore the innovative concept of measure-theoretic Reeb graphs in this 56-minute lecture from the Applied Algebraic Topology Network. Delve into a novel construction of Reeb graphs that incorporates measures, enhancing their robustness in representing topological features of scalar fields. Learn about the stability of Reeb graphs with local smoothing and their application to metric measure spaces. Discover how these advanced techniques utilize distance to measure and kernel distance to measure, providing a more comprehensive understanding of scalar functions on topological spaces.
Overview
Syllabus
Qingsong Wang (06/19/24): Measure Theoretic Reeb Graphs
Taught by
Applied Algebraic Topology Network
Related Courses
-
Stability of Reeb Ordering Method in the Framework of Pospaces
-
Tomoo Yokoyama - Generalizations of Morse Graph of Flows and Reeb Graph of Hamiltonian Flows
-
Computation of Reeb Graphs in a Semi-Algebraic Setting
-
The Mapper Algorithm and Reeb Graphs
-
Antonio Rieser - Algebraic Topology for Graphs and Mesoscopic Spaces
-
The Reeb Graph of a Smooth Function Encodes the Function Class and Manifold Type
