For the first 2-3 weeks, I will use these notes giving an overview of differential geometry and gauge theory (focus), as well as classical-to-quantum mechanics (a little). The bundle theory part will be covered in greater detail in the middle of the course.
Subsequently, we will roughly follow (notes ), Weeks 3-15, with some changes in topics.
The examinable content is covered in the lectures, while the above notes contain a bit of extra material.
Monday 9 June 2025, 8.30am, Teaching Building 2, Room 315. This will be a closed book exam.
55% final exam. 45% take-home assignments (~3)
(Assignment 1) Due 17 March, 8am.
(Assignment 2) Due 14 April, 8am.
(Assignment 3) Due 26 May, 8am.
Reed, M., Simon, B.: Methods of Modern Mathematical Physics, Vol. 1. Functional Analysis. and Vol. II. Fourier analysis, Self-adjointness, Acad. Press, 1980, 1975
Moretti, V.: Spectral Theory and Quantum Mechanics, Springer, 2013
Strocchi, F.: An Introduction to the Mathematical Structure of Quantum Mechanics, World Scientific, 2005
Arveson, W.: A short course on spectral theory, GTM 209, 2002
Baez, J., Muniain, J.P.: Gauge Fields, Knots, and Gravity, World Scientific, 1994
Bleecker, D., Booss-Bavnbek, B.: Index theory with applications to mathematics and physics. International Press, 2013
Choquet-Bruhat, Y., Dewitt-Morette, C.: Analysis, manifolds, and physics. Part I: Basics. North Holland, 1982
Naber, G.: Topology, Geometry, and Gauge Fields. Foundations. Texts in Appl. Math., Springer, 2011
Lee, J.M.: Introduction to smooth manifolds. GTM 218, Springer, 2013
Friedrich, T.: Dirac operators in Riemannian geometry. GSM 25, AMS, 2000
Folland, G.B.: Quantum field theory. A tourist guide for mathematicians. Math. Surveys and Monogr., 149, 2008
Linear algebra, real analysis, metric and topological spaces
Basic abstract algebra (especially groups)
Idea of differentiable manifolds
Familiarlity with Hilbert spaces (at least semi-rigorously)
Exposure to theoretical physics is helpful, but not compulsory.