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Mathematical Physics Lecture - 230117
Kevin Costello - Perimeter Institute for Theoretical Physics
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Mathematical Physics Lecture - 230118
Kevin Costello - Perimeter Institute for Theoretical Physics
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Mathematical Physics Lecture - 230119
Kevin Costello - Perimeter Institute for Theoretical Physics
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Mathematical Physics Lecture - 230124
Kevin Costello - Perimeter Institute for Theoretical Physics
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Mathematical Physics Lecture - 230126
Kevin Costello - Perimeter Institute for Theoretical Physics
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Mathematical Physics Lecture - 230127
Kevin Costello - Perimeter Institute for Theoretical Physics
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Mathematical Physics Lecture - 230131
Kevin Costello - Perimeter Institute for Theoretical Physics
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Mathematical Physics Lecture - 230202
Kevin Costello - Perimeter Institute for Theoretical Physics
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Mathematical Physics Lecture - 230207
Kevin Costello - Perimeter Institute for Theoretical Physics
This course will cover the mathematical structure underlying classical gauge theory. Previous knowledge of differential geometry is not required. Topics covered in the course include: introduction to manifolds, symplectic manifolds, introduction to Lie groups and Lie algebras; deformation quantisation and geometric quantisation; the matematical structure of field theories; scalar field theory; geometric picture of Yang-Mills theory; symplectic reduction.
If time permits, we may also look at the description of gauge theory in terms of principal bundles and the topological aspects of gauge theory.