1 option
Geometry, Topology and Operator Algebras : Global Analysis, Invariants and Their Significance in Theoretical Physics / edited by Alexander Cardona, Andrés F. Reyes Lega.
Springer Nature - Springer Physics and Astronomy (R0) eBooks 2025 English International Available online
View online- Format:
- Book
- Series:
- Mathematical Physics Studies, 2352-3905
- Language:
- English
- Subjects (All):
- Mathematical physics.
- Geometry, Algebraic.
- Number theory.
- Condensed matter.
- Theoretical, Mathematical and Computational Physics.
- Mathematical Physics.
- Mathematical Methods in Physics.
- Algebraic Geometry.
- Number Theory.
- Condensed Matter Physics.
- Local Subjects:
- Theoretical, Mathematical and Computational Physics.
- Mathematical Physics.
- Mathematical Methods in Physics.
- Algebraic Geometry.
- Number Theory.
- Condensed Matter Physics.
- Physical Description:
- 1 online resource (XIII, 281 p. 15 illus., 11 illus. in color.)
- Edition:
- 1st ed. 2025.
- Place of Publication:
- Cham : Springer Nature Switzerland : Imprint: Springer, 2025.
- Summary:
- 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.
- Contents:
- 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.
- ISBN:
- 3-031-82319-2
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