Overview
- Collects current research on quantitative Tamarkin theory into one convenient, self-contained textbook
- Provides readers with an accessible categorical approach to microlocal sheaf theory that contrasts with established algebraic analysis methods
- Reviews key background material in the opening chapters, making it accessible to a wide audience of interested readers
Part of the book series: CRM Short Courses (CRMSC)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
Keywords
- Tamarkin category theory
- Tamarkin microlocal category
- Tamarkin math
- Tamarkin category
- Symplectic geometry
- Symplectic topology
- Symplectic homology
- Microlocal sheaf theory
- Microlocal sheaf theory applications
- Microlocal sheaf theory quantitative symplectic topology
- Quantitative symplectic topology
- Non-squeezing theorem
- Sheaf quantization
- Singular support
- Persistence modules
- Sheaf barcode
- Hofer geometry
- partial differential equations
About this book
This textbook offers readers a self-contained introduction to quantitative Tamarkin category theory. Functioning as a viable alternative to the standard algebraic analysis method, the categorical approach explored in this book makes microlocal sheaf theory accessible to a wide audience of readers interested in symplectic geometry. Much of this material has, until now, been scattered throughout the existing literature; this text finally collects that information into one convenient volume.
After providing an overview of symplectic geometry, ranging from its background to modern developments, the author reviews the preliminaries with precision. This refresher ensures readers are prepared for the thorough exploration of the Tamarkin category that follows. A variety of applications appear throughout, such as sheaf quantization, sheaf interleaving distance, and sheaf barcodes from projectors. An appendix offers additional perspectives by highlighting further useful topics.Quantitative Tamarkin Theory is ideal for graduate students interested in symplectic geometry who seek an accessible alternative to the algebraic analysis method. A background in algebra and differential geometry is recommended.
This book is part of the "Virtual Series on Symplectic Geometry"
http://www.springer.com/series/16019
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Authors and Affiliations
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Bibliographic Information
Book Title: Quantitative Tamarkin Theory
Authors: Jun Zhang
Series Title: CRM Short Courses
DOI: https://doi.org/10.1007/978-3-030-37888-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-37887-5Published: 10 March 2020
Softcover ISBN: 978-3-030-37890-5Published: 10 March 2021
eBook ISBN: 978-3-030-37888-2Published: 09 March 2020
Series ISSN: 2522-5200
Series E-ISSN: 2522-5219
Edition Number: 1
Number of Pages: X, 146
Number of Illustrations: 63 b/w illustrations
Topics: Differential Geometry, Partial Differential Equations, Dynamical Systems and Ergodic Theory, Algebraic Topology