Noncommutative geometry of gravity, strings and fields: A panoramic overview
Abstract
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key mathematical approaches presented include operator algebras such as $C^*$-algebras, K-theory, spectral geometry, quantum groups, and deformation quantization. Physical application areas considered include string theory, quantum field theory, and the Standard Model, as well as certain condensed matter systems.
Fields of Study & Subjects
Noncommutative and Quantum Gravity Theories
Advanced Operator Algebra Research
Black Holes and Theoretical Physics
Publication details
- Journal / source
- EMS series of lectures in mathematics
- Pages
- 315–388
- Publication date
- 23 June 2026
- Language
- EN
- Document type
- Book chapter