Differential geometry

Overview

Prof C M Hull FRS

The course will use examples from mechanics, quantum theory, electromagnetism, general relativity and gauge theory to illustrate these ideas and their application in physics.

Manifolds
The idea of a manifold. Tangent vectors, vector fields and flows. Differential forms and exterior calculus. Differential forms and exterior calculus. 

Integration, Stokes' Theorem and Cohomology
Integration of differential forms. Stokes' theorem. Cohomology and de Rham's theorem.

Riemannian Geometry
Volume forms and non-coordinate bases. The Hodge star. Connections, covariant differentiation, torsion and curvature. Cartan's structure equations. 

Fibre bundles
The idea of a bundle. Vector and principle bundles.

 

 

Lecture Notes

Lecture Notes 2016

Books for the course.

Past papers

Important: Course material has changed so the content of past papers from 2012 and before is not representative of this year's course. In particular, Lie groups and homology are no longer part of the course.