Ricci Curvature and Ricci Flow for Graphs and Hypergraphs
Published in PhD Dissertation, University of Illinois at Chicago, 2024
My doctoral dissertation, advised by Bhaskar DasGupta, on discretizing notions of curvature and curvature-driven flows for network-theoretic structures. The thesis covers discrete curvature on graphs and hypergraphs, Ollivier-Ricci curvature, Ricci flow, and the extension of Ricci flow to hypergraphs, with applications to identifying influential structures in real-world networks.