Topology in Physics

6 EC

Semester 2, period 4, 5

5354TOIP6Y

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 1Master Mathematics, specialization Analysis and Dynamical Systems, year 1Master Mathematics, specialization Mathematical Physics, year 1Master Mathematics, specialization Stochastics , year 1Master Physics and Astronomy (joint degree), track General Physics and Astronomy, Master Mathematics, specialisation Discrete Mathematics and Quantum Information, year 1Double master Mathematics and Physics, Master Quantum Computer Science,

Course manual 2024/2025

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.

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

Requirements concerning attendance (OER-B).

  • In addition to, or instead of, classes in the form of lectures, the elements of the master’s examination programme often include a practical component as defined in article A-1.2 of part A. The course catalogue contains information on the types of classes in each part of the programme. Attendance during practical components is mandatory.

    • Additional requirements for this course:

    For the homework grade, the worst three hand-in results will not be counted. (As a result, students can choose not to hand in up to three times - though this is of course not advised, as excercise sets that are handed in will often receive some feedback from the TAs.)

    Assessment

    Item and weight Details

    Final grade

    70%

    Tentamen

    		Must be ≥ 5

    30%

    Homework

    Final grade after retake

    70%

    Hertentamen

    		Must be ≥ 5

    30%

    Homework

    Assignments

    For the homework, you are invited and even encouraged to discuss with your fellow students. However, the written down solution should be 100% your own.

    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

    Additional information

    Further information about the course can also be found on its Canvas page.

    Contact information

    Coordinator

    • dr. Marcel Vonk