Groups, Invariants, Integrals, and Mathematical Physics: The Wisła 20-21 Winter School and Workshop (Tutorials, Schools, and Workshops in the Mathematical Sciences) - Hardcover

Hardcover

ISBN 10: 3031256654 ISBN 13: 9783031256653

Publisher: Birkhäuser, 2023

Synopsis

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.

About this title

From the Back Cover

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.

Edition details

• Publisher: Birkhäuser
• Publication date: 2023
• Language: English
• ISBN 10: 3031256654
• ISBN 13: 9783031256653
• Binding: Hardcover
• Number of pages: 266
• Editor: Ulan Maria, Hronek Stanislav