A quantum field theory is deemed topological if it exhibits the remarkable property of being independent of any background metric. In contrast to most other types of quantum field theories, topological quantum field theories possess a welldefined mathematical framework, tracing its roots back to the pioneering work of Atiyah in 1988. The mathematical tools employed to define and study topological quantum field theories encompass concepts from category theory, homotopy theory, topology, and algebra.
In this course, we will delve into the mathematical foundations of this field, explore examples and classification results, especially in lower dimensions. Subsequently, we will explore more advanced aspects, such as invertible theories, defects, the cobordism hypothesis, or state sum models in dimensions 3 and 4 (including TuraevViro and DouglasReutter models), depending on the interests of the audience.
Today, the mathematics of topological quantum field theories has found numerous applications in physics. Recent applications include the study of anomalies, noninvertible symmetries, the classification of topological phases of matter, and lattice models. The course aims to provide the necessary background for understanding these applications.
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Topological Quantum Field Theories Lecture 20231201
Lukas Mueller Perimeter Institute for Theoretical Physics

Topological Quantum Field Theories Lecture 20231124
Lukas Mueller Perimeter Institute for Theoretical Physics

Topological Quantum Field Theories Lecture 20231110
Lukas Mueller Perimeter Institute for Theoretical Physics

Topological Quantum Field Theories Lecture 20231103
Lukas Mueller Perimeter Institute for Theoretical Physics

Topological Quantum Field Theories Lecture 20231027
Lukas Mueller Perimeter Institute for Theoretical Physics

Topological Quantum Field Theories Lecture 20231020
Lukas Mueller Perimeter Institute for Theoretical Physics

Topological Quantum Field Theories Lecture 20231013
Lukas Mueller Perimeter Institute for Theoretical Physics

Topological Quantum Field Theories Lecture 20231006
Lukas Mueller Perimeter Institute for Theoretical Physics