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Analysis and Geometry on Graphs and Manifolds

$115.00 (C)

Part of London Mathematical Society Lecture Note Series

Bobo Hua, Yanhui Su, David Cushing, Shiping Liu, Florentin Munch, Norbert Peyerimho, Józef Dodziuk, Colette Anné, Olaf Post, Peter Stollmann, Christian Rose, Massimo A. Picardello, Wolfgang Woess, Joe P. Chen, Wilfried Huss, Ecaterina Sava-Huss, Alexander Teplyaev, Daniel Lenz, Matthias Keller, Yehuda Pinchover, Felix Pogorzelski, Lior Alon, Michael Bersudsky, Sebastian Egger, Rami Band, Marcel Schmidt, Ana Khukhro, Alain Valette, Ori Parzanchevski, Andrzej Żuk, David Damanik, Jake Fillman, Christoph Schumacher, Fabian Schwarzenberger, Ivan Veselic
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  • Date Published: October 2020
  • availability: In stock
  • format: Paperback
  • isbn: 9781108713184

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About the Authors
  • 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.

    • Displays interactions between various areas of mathematics (geometry, spectral theory and stochastics) so readers from different backgrounds can find common approaches to various problems
    • Discusses both the discrete and continuum settings so readers see the parallels and disparities between these two settings
    • Gives thorough overviews of certain topics as well as brief glances at specific problems to allow readers to get a foothold in various areas of mathematics
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    Product details

    • Date Published: October 2020
    • format: Paperback
    • isbn: 9781108713184
    • length: 492 pages
    • dimensions: 228 x 151 x 27 mm
    • weight: 0.72kg
    • availability: In stock
  • Table of Contents

    1. Infinite planar graphs with nonnegative combinatorial curvature Bobo Hua and Yanhui Su
    2. Curvature calculations for antitrees David Cushing, Shiping Liu, Florentin Munch and Norbert Peyerimho
    3. Gromov-Lawson tunnels with estimates Józef Dodziuk
    4. Norm convergence of the resolvent for wild perturbations Colette Anné and Olaf Post
    5. Manifolds with Ricci curvature in the Kato class: heat kernel bounds and applications Peter Stollmann and Christian Rose
    6. Multiple boundary representations of λ – harmonic functions on trees Massimo A. Picardello and Wolfgang Woess
    7. Internal DLA on Sierpinski gasket graphs Joe P. Chen, Wilfried Huss, Ecaterina Sava-Huss and Alexander Teplyaev
    8. Universal lower bounds for Laplacians on weighted graphs Daniel Lenz and Peter Stollmann 9. On Hardy inequalities on graphs and manifolds Matthias Keller, Yehuda Pinchover and Felix Pogorzelski
    10. Neumann domains on manifolds and graphs Lior Alon, Michael Bersudsky, Sebastian Egger and Rami Band
    11. On the existence and uniqueness of self-adjoint realizations of discrete (magnetic) Schrödinger operators Marcel Schmidt
    12. Box spaces: geometry of finite quotients Ana Khukhro and Alain Valette
    13. Ramanujan graphs and digraphs Ori Parzanchevski
    14. From partial differential equations to groups Andrzej Żuk
    15. Spectral properties of limit-periodic operators David Damanik and Jake Fillman
    16. Uniform existence of the IDS on lattices and groups Christoph Schumacher, Fabian Schwarzenberger and Ivan Veselic.

  • Editors

    Matthias Keller, Universität Potsdam, Germany
    Matthias Keller is a Professor of Mathematics at the University of Potsdam. He has contributed to books including Random Walks, Boundaries and Spectra (2011) and Modern Approaches to Discrete Curvature (2017).

    Daniel Lenz, Universität Potsdam, Germany
    Daniel Lenz is a Professor of Mathematics at the Friedrich-Schiller University Jena. He has written numerous papers and previously contributed to Groups, Graphs and Random Walks (Cambridge, 2017).

    Radoslaw K. Wojciechowski, York College of the City University of New York
    Radoslaw K. Wojciechowski is an Associate Professor at the City University of New York and a member of the American Mathematical Society. He currently has a Simons Collaboration Grant for Mathematicians and previously was awarded a National Science Foundation Conferences and Workshops in the Mathematical Sciences Grant. He has contributed to the book Random Walks, Boundaries and Spectra (2011).

    Contributors

    Bobo Hua, Yanhui Su, David Cushing, Shiping Liu, Florentin Munch, Norbert Peyerimho, Józef Dodziuk, Colette Anné, Olaf Post, Peter Stollmann, Christian Rose, Massimo A. Picardello, Wolfgang Woess, Joe P. Chen, Wilfried Huss, Ecaterina Sava-Huss, Alexander Teplyaev, Daniel Lenz, Matthias Keller, Yehuda Pinchover, Felix Pogorzelski, Lior Alon, Michael Bersudsky, Sebastian Egger, Rami Band, Marcel Schmidt, Ana Khukhro, Alain Valette, Ori Parzanchevski, Andrzej Żuk, David Damanik, Jake Fillman, Christoph Schumacher, Fabian Schwarzenberger, Ivan Veselic

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