Course manual 2025/2026

Course content

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:

Descriptions of gauge fields: differential forms, fiber bundles and connections.
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 an anomalies.

Study materials

Literature

Besides the lecture notes (now in book form) no specific book is used, but we recommend the book by Nakahara, 'Geometry, Topology and Physics' as background material.

Syllabus

Lecture notes (now in book form) will be provided for each lecture.

Objectives

Students will learn several mathematical methods from topology and how to apply those methods to physics problems.
Vice versa, students will learn how to apply intuition from physics as a useful mathematical tool.

Teaching methods

Lecture
Seminar
Self-study

Learning activities

Activity	Number of hours
Hoorcollege	34
Werkcollege	34
Zelfstudie	100

Attendance

Some course components require compulsory attendance. If compulsory attendance applies, this will be indicated in the Course Catalogue which can be consulted via the UvA-website. The rationale for and implementation of this compulsory attendance may vary per course and, if applicable, is included in the Course Manual.

Assessment

Item and weight	Details
Final grade
80% Tentamen
20% Homework
Final grade after retake
80% Hertentamen
20% Homework

Homework is not compulsory but strongly recommended. If all three homework sets are handed in, the average grade counts towards 20% of the final grade. (But only if this improves the grade, which is generally the case.) If homework is counted, the exam grade should still be 5 or higher to pass the course.

Assignments

Three homework sets, after lecture 4 or 5, lecture 8, and lecture 11 or 12. The hand-in date is one or sometimes two weeks afterwards. Communicating with fellow students about the problems is allowed (and even encouraged), but the written solution must be your own work. See under "Assesment" for the grading of the homework.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Weeknummer	Onderwerpen	Studiestof
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16

Owner	Master Physics and Astronomy (joint degree)
Coordinator	dr. Marcel Vonk
Part of	Master Physics and Astronomy, track Theoretical Physics, Master Mathematics, specialization Algebra and Geometry, year 1 Master Mathematics, specialization Analysis and Dynamical Systems, year 1 Master Mathematics, specialization Mathematical Physics, year 1 Master Mathematics, specialization Stochastics , year 1 Master Physics and Astronomy (joint degree), track General Physics and Astronomy, Master Mathematics, specialisation Discrete Mathematics and Quantum Information, year 1 Double master Mathematics and Physics, Master Quantum Computer Science,

Topology in Physics