Groups, Invariants, Integrals, and Mathematical Physics : The Wisła 20-21 Winter School and Workshop / edited by Maria Ulan, Stanislav Hronek.

Format:

Book

Author/Creator:

Ulan, Maria.

Contributor:

Hronek, Stanislav.

Series:

Tutorials, Schools, and Workshops in the Mathematical Sciences, 2522-0977

Language:

English

Subjects (All):

Mathematical physics.

Group theory.

Topological groups.

Lie groups.

Differential equations.

Algebra, Homological.

Mathematical Physics.

Group Theory and Generalizations.

Topological Groups and Lie Groups.

Differential Equations.

Category Theory, Homological Algebra.

Local Subjects:

Mathematical Physics.

Group Theory and Generalizations.

Topological Groups and Lie Groups.

Differential Equations.

Category Theory, Homological Algebra.

Physical Description:

1 online resource (263 pages)

Edition:

1st ed. 2023.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2023.

Summary:

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.

Contents:

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.

Notes:

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Ulan, Maria Groups, Invariants, Integrals, and Mathematical Physics

ISBN:

9783031256660

3031256662

OCLC:

1381093506