• Lecturer: Florentin Münch
• Date: Wednesday, 15.00
• Room: MPI MiS A3 01
• Keywords: graphs, curvature, heat equation
• Prerequisites: Basic analysis and linear algebra

Abstract

In this lecture, we give an overview of recent developments concerning discrete Ricci curvature. Discrete Ricci curvature has proven to be a useful tool in network analysis. It has been applied for detecting local clusters within a network and for finding most important connections between two nodes. The course focuses on the theoretical background of discrete Ricci curvature. Particularly, we study relations between curvature bounds, random walks and the heat equation. As applications, we can estimate the spectral gap of the graph Laplacian and derive geometric properties as diameter bounds, Gaussian measure concentration and volume growth in terms of the curvature.

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