Networks’ emergence as an ideal setting for studying complex systems brought enormous interest in extending powerful harmonic analysis (HA) tools from Euclidean spaces to graphs. Most efforts focused on the graph Laplacian’s eigendecomposition, producing results such as the graph Fourier transform. Recently, the same endeavor moved to higher-order network structures—simplicial simplexes. We survey classical Fourier analysis and its graph extensions before presenting new developments and challenges of HA on simplicial complexes based on the Hodge Laplacian.
Harmonic Analysis on Simplicial Simplexes: How far could we take it?
Karamatou Yacoubou Djima, Wellesley CollegeAuthors: Karamatou Yacoubou Djima
2023 AWM Research Symposium
Pure and Applied Talks by Mathematicians Enhancing Diversity in Graduate Education (EDGE) [Organized by Quiyana M. Murphy and Sofía Martínez Alberga]