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＜E-Book＞
Groups, Invariants, Integrals, and Mathematical Physics : The Wisła 20-21 Winter School and Workshop / edited by Maria Ulan, Stanislav Hronek
(Tutorials, Schools, and Workshops in the Mathematical Sciences. ISSN:25220977)

Edition	1st ed. 2023.
Publisher	(Cham : Springer Nature Switzerland : Imprint: Birkhäuser)
Year	2023
Language	English
Size	XV, 251 p. 29 illus., 6 illus. in color : online resource
Authors	Ulan, Maria editor Hronek, Stanislav editor SpringerLink (Online service)
Subjects	LCSH:Mathematical physics LCSH:Group theory LCSH:Topological groups LCSH:Lie groups LCSH:Differential equations LCSH:Algebra, Homological FREE:Mathematical Physics FREE:Group Theory and Generalizations FREE:Topological Groups and Lie Groups FREE:Differential Equations FREE:Category Theory, Homological Algebra
Notes	Lychagin, V., Roop, M., Differential Invariants in Algebra -- Rubtsov, V., Suchánek, R., Lectures on Poisson Algebras -- Suchánek,R., Some Remarks on Multisymplectic and Variational Nature of Monge-Ampère Equations in Dimension Four -- Ruiz, A., Muriel, C., Generalized Solvable Structures Associated to Symmetry Algebras Isomorphic to $\mathfrak{gl}(2,\mathbb{R}) \ltimes \mathbb{R}$ -- Maksymenko, S., Nikitchenko, O., Fundamental Groupoids and Homotopy Types of Non-Compact Surfaces -- Barth, L. S., A Geometric Framework to Compare Classical Field Theories 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 systems of 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 HTTP:URL=https://doi.org/10.1007/978-3-031-25666-0

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