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Explore a mathematical lecture introducing a generalized Gromov-Hausdorff distance for comparing chromatic metric spaces, which extend traditional metric spaces by incorporating coloring functions that associate points with specific colors. Learn about the theoretical framework building upon chromatic point clouds from Cultrera di Montesano et al. (2022) and discover how the six-pack collection of persistence diagrams extracts homological information about interactions between colored subsets. Examine the fundamental properties of this new distance measure and understand its validation through establishing stability of the six-pack with respect to the proposed distance. Gain insights into collaborative research in applied algebraic topology through work conducted with Ondřej Draganov and Sophie Rosenmeier, focusing on advanced mathematical concepts in metric geometry and topological data analysis.
