Discrete Geometric Analysis

This is an expository article on discrete geometric analysis based on the lectures which the author gave at Gregynog Hall, University of Wales, as an activity of the Project “Analysis on graphs and its applications” in the Issac Newton Institute. Topics are selected to illustrate the nature of the field; that is, we focus upon analysis on graphs with a geometric flavor such as graph versions of harmonic theory and spectral geometry of Laplacians. Zeta functions and random walks are also discussed from a geometric viewpoint.

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