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Geometry, topology and operator alge...

Cardona, Alexander.

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Geometry, topology and operator algebras = global analysis, invariants and their significance in theoretical physics /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Geometry, topology and operator algebras/ edited by Alexander Cardona, Andrés F. Reyes Lega.
其他題名:	global analysis, invariants and their significance in theoretical physics /
其他作者:	Cardona, Alexander.
出版者:	Cham :Springer Nature Switzerland : : 2025.,
面頁冊數:	xiii, 281 p. :ill. (chiefly color), digital ;24 cm.
內容註:	Geometric structures, invariants and their uses in physics by A. Cardona and A.F. Reyes-Lega -- Lectures on the Euler characteristic of affine manifolds by Camilo Arias-Abad and Sebastian Velez-Vasquez -- Elliptic Curves by Philip Candelas -- The arithmetic of Calabi-Yau varieties, by Xenia de la Ossa -- Foliations and operator algebras by Georges Skandalis -- Pseudo-differential operators on groups and nonharmonic analysis, by Michael Ruzhansky -- Mathematical Foundations of Topological Matter, by Manuel Asorey.
Contained By:	Springer Nature eBook
標題:	Mathematical physics. -
電子資源:	https://doi.org/10.1007/978-3-031-82319-0
ISBN:	9783031823190

Geometry, topology and operator algebras = global analysis, invariants and their significance in theoretical physics /
Geometry, topology and operator algebrasglobal analysis, invariants and their significance in theoretical physics /[electronic resource] :edited by Alexander Cardona, Andrés F. Reyes Lega. - Cham :Springer Nature Switzerland :2025. - xiii, 281 p. :ill. (chiefly color), digital ;24 cm. - Mathematical physics studies,2352-3905. - Mathematical physics studies..

Geometric structures, invariants and their uses in physics by A. Cardona and A.F. Reyes-Lega -- Lectures on the Euler characteristic of affine manifolds by Camilo Arias-Abad and Sebastian Velez-Vasquez -- Elliptic Curves by Philip Candelas -- The arithmetic of Calabi-Yau varieties, by Xenia de la Ossa -- Foliations and operator algebras by Georges Skandalis -- Pseudo-differential operators on groups and nonharmonic analysis, by Michael Ruzhansky -- Mathematical Foundations of Topological Matter, by Manuel Asorey.

This book offers a comprehensive exploration of contemporary intersections between geometry, topology, and theoretical physics, emphasizing their mathematical foundations and applications. Originating from lectures presented by experts during two summer schools held in Villa de Leyva, Colombia, the book reflects the synergy between global analysis, operator algebras, and their role in modern physics. The chapters present state-of-the-art developments on a wide range of topics: the geometry and topology of foliations, affine manifolds, C*-algebras, and the pseudo-differential calculus of boundary value problems. These are enriched by applications to the theory of topological quantum matter. The book is suitable for graduate students and researchers, offering detailed introductions to advanced topics such as the longitudinal index theorem for foliations, the geometry of the Poincaré half-space in a C*-algebra, and mathematical frameworks for topological matter. With a balance of foundational material and novel insights, it serves as both a learning resource and a reference for advanced studies at the intersection of mathematics and physics.

ISBN: 9783031823190

Standard No.: 10.1007/978-3-031-82319-0doiSubjects--Topical Terms:

516853
Mathematical physics.

LC Class. No.: QC20.7.G44

Dewey Class. No.: 530.156

Geometry, topology and operator algebras = global analysis, invariants and their significance in theoretical physics /
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520 $a This book offers a comprehensive exploration of contemporary intersections between geometry, topology, and theoretical physics, emphasizing their mathematical foundations and applications. Originating from lectures presented by experts during two summer schools held in Villa de Leyva, Colombia, the book reflects the synergy between global analysis, operator algebras, and their role in modern physics. The chapters present state-of-the-art developments on a wide range of topics: the geometry and topology of foliations, affine manifolds, C*-algebras, and the pseudo-differential calculus of boundary value problems. These are enriched by applications to the theory of topological quantum matter. The book is suitable for graduate students and researchers, offering detailed introductions to advanced topics such as the longitudinal index theorem for foliations, the geometry of the Poincaré half-space in a C*-algebra, and mathematical frameworks for topological matter. With a balance of foundational material and novel insights, it serves as both a learning resource and a reference for advanced studies at the intersection of mathematics and physics.
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