Analysis and Geometry on Graphs and Manifolds
“Analysis and Geometry on Graphs and Manifolds” by Matthias Keller, published by Cambridge University Press on August 20, 2020, is a comprehensive volume comprising 492 pages. This edition presents a collection of contributions from a 2017 conference at the University of Potsdam, emphasizing the interplay between geometry, spectral theory, and stochastics, which has significantly influenced modern mathematics.
Readers will find a diverse range of survey articles that provide an overview of various topics, including curvature and the effects of geometry on the spectrum. The book explores both discrete and continuous settings, appealing to researchers and graduate students in geometric analysis. Additionally, it features shorter articles that delve into specific techniques and problems, allowing for a focused examination of key concepts in mathematics, calculus, and functional analysis.
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The interplay of geometry, spectral theory and stochastics has a long and fruitful history, and is the driving force behind many developments in modern mathematics. Bringing together contributions from a 2017 conference at the University of Potsdam, this volume focuses on global effects of local properties. Exploring the similarities and differences between the discrete and the continuous settings is of great interest to both researchers and graduate students in geometric analysis. The range of survey articles presented in this volume give an expository overview of various topics, including curvature, the effects of geometry on the spectrum, geometric group theory, and spectral theory of Laplacian and Schrödinger operators. Also included are shorter articles focusing on specific techniques and problems, allowing the reader to get to the heart of several key topics.
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