Geometry, Topology and Operator Algebras
Global Analysis, Invariants and Their Significance in Theoretical Physics
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Beschreibung
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.
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.
Based on lecture notes by experts in their fields Includes the necessary background material for the more advanced topics Hints at new promising applications and emerging areas of research
Autor*in
Alexander Cardona
Themen in »Geometry, Topology and Operator Algebras«
Elliptic curves Calabi-Yau varieties topological quantum matter mirror symmetry renormalization in FT topological phases of matter fermionic quadratic chains entanglement entropy Riemann surfaces Potts model complex geometry affine manifolds bundles motivic approach string theory