Some background knowledge in both physics and mathematics is assumed. On the mathematics side, we will assume some basic knowledge of:
• Lie groups (following the simultaneous course in Lie Groups at the UvA math department is sufficient)
• Topology and cohomology (cohomology will be briefly reviewed during the course)
On the physics side, we will assume some basic knowledge of:
• Classical mechanics
• Quantum mechanics
• Quantum field theory
If you would like to know whether your background knowledge suffices to follow this course (or what you should do as a preparation if this is not the case), feel free to contact one of the lecturers.
Aim of the course
This course is aimed at both physics and mathematics students. The aim of the course is to demonstrate how many current mathematical methods, that can be very broadly classified as "topological", play an important role in quantum field theory and other areas of modern physics, and conversely how ideas from physics are applied in modern mathematics. The course will focus on the following topics:
• Characteristic classes (Chern-Weil)
• Fermions and Dirac operators
• Index theorems and their "physics proof"
• If time permits, several further topics on the border line of mathematics and physics could be covered, such as topological quantum field theories, Chern-Simons theories and knot invariants.
Exam and homework
A written exam at the end of the course. Each week there will be homework consisting typically of one of the exercises of the exercise class. Homework counts as 30% (best 11 out of 14).
Lecture Notes / Literature
We will provide lecture notes.
Marcel Vonk and Hessel Posthuma