Title Groups, invariants, integrals, and mathematical physics : the Wisła 20-21 Winter School and Workshop / Maria Ulan, Stanislav Hronek, editors

Published Cham : Birkhäuser, 2023

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Description 1 online resource Series Tutorials, schools, and workshops in the mathematical sciences Baltic Institute of Mathematics collection Tutorials, schools, and workshops in the mathematical sciences. Contents Lychagin, V., Roop, M., Differential Invariants in Algebra -- Rubtsov, V., Suchnek, R., Lectures on Poisson Algebras -- Suchnek,R., Some Remarks on Multisymplectic and Variational Nature of Monge-Ampre 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 Summary This volume presents lectures given at the Wisa 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-Ampre 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 Analysis Physics Science Bibliography Includes bibliographical references Notes Online resource; title from PDF title page (SpringerLink, viewed June 14, 2023) Subject Differential algebra -- Congresses Mathematical physics -- Congresses Differential algebra Mathematical physics Àlgebra diferencial. Física matemàtica. Genre/Form Electronic books proceedings (reports) Conference papers and proceedings Conference papers and proceedings. Actes de congrès. Llibres electrònics. Form Electronic book Author Ulan, Maria Hronek, Stanislav Wisła (Winter School) (2021 : Online) ISBN 9783031256660 3031256662

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