Overview
- Features lecture notes, surveys, and original research, ideal for pedagogical use independently or in the classroom
- Covers a wide variety of topics, using both theoretical and applied approaches
- Provides an accessible introduction to topics spanning differential geometry, differential equations and category theory
Part of the book series: Tutorials, Schools, and Workshops in the Mathematical Sciences (TSWMS)
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Table of contents (6 chapters)
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Front Matter
Keywords
About this book
This volume presents lectures given at the Wisła 20-21 Winter School and Workshop: Groups, Invariants, Integrals, and Mathematical Physics, organized by the Baltic Institute of Mathematics. The lectures were dedicated to differential invariants – with a focus on Lie groups, pseudogroups, and their orbit spaces – and Poisson structures in algebra and geometry and are included here as lecture notes comprising the first two chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and category theory. Specific topics covered include:
- The multisymplectic and variational nature of Monge-Ampère equations in dimension four
- Integrability of fifth-order equations admitting a Lie symmetry algebra
- Applications of the van Kampen theorem for groupoids to computation of homotopy types of striped surfaces
- A geometric framework to compare classical systemsof PDEs in the category of smooth manifolds
Groups, Invariants, Integrals, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry and category theory is assumed.
Editors and Affiliations
Bibliographic Information
Book Title: Groups, Invariants, Integrals, and Mathematical Physics
Book Subtitle: The Wisła 20-21 Winter School and Workshop
Editors: Maria Ulan, Stanislav Hronek
Series Title: Tutorials, Schools, and Workshops in the Mathematical Sciences
DOI: https://doi.org/10.1007/978-3-031-25666-0
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-25665-3Published: 02 June 2023
Softcover ISBN: 978-3-031-25668-4Due: 19 August 2023
eBook ISBN: 978-3-031-25666-0Published: 31 May 2023
Series ISSN: 2522-0969
Series E-ISSN: 2522-0977
Edition Number: 1
Number of Pages: XV, 251
Number of Illustrations: 23 b/w illustrations, 6 illustrations in colour
Topics: Mathematical Physics, Group Theory and Generalizations, Topological Groups, Lie Groups, Analysis, Category Theory, Homological Algebra