260081 VU Topological quantum field theory (2022W)
Continuous assessment of course work
Labels
Registration/Deregistration
Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
- Registration is open from Th 01.09.2022 08:00 to Mo 26.09.2022 07:00
- Deregistration possible until Fr 21.10.2022 23:59
Details
max. 15 participants
Language: English
Lecturers
Classes (iCal) - next class is marked with N
Tuesday
11.10.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Thursday
13.10.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Tuesday
18.10.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Thursday
20.10.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Tuesday
25.10.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Thursday
27.10.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Thursday
03.11.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Tuesday
08.11.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Thursday
10.11.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Tuesday
15.11.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Thursday
17.11.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Tuesday
22.11.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Thursday
24.11.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Tuesday
29.11.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Thursday
01.12.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Tuesday
06.12.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Tuesday
13.12.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Thursday
15.12.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Tuesday
10.01.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Thursday
12.01.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Tuesday
17.01.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Thursday
19.01.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Tuesday
24.01.
11:15 - 12:45
Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
Information
Aims, contents and method of the course
This course is an introduction to an axiomatic, functorial approach to topological quantum field theory (TQFT). In physics, TQFT offers a rigorous and (arguably) elegant framework to study and develop some aspects of quantum field theory in general, and to describe specific phases of matter and models of topological quantum computation in particular. Mathematically, TQFT provides algebraic invariants of manifolds (often with extra structure such as orientation, spin, or knots).We will start with a concise review of (desired) properties of path integrals, and explain how they motivate the axiomatic definition of TQFTs in terms of monoidal categories and functors. These and related notions will be introduced (with no special prior knowledge assumed), along with various illustrating examples. Some of the general theory of TQFTs in arbitrary "spacetime" dimension d will be developed. After that we will mostly consider the cases d=2 (related to string theory and conformal field theory) and d=3 (related to topological phases of matter and quantum computation). In particular, we will study "state sum models" and "sigma models".Prerequisites: Familiarity with linear algebra, some basic ideas about quantum physics, a fondness for algebraic structures, and a mere interest in the functorial approach to quantum field theory (the relevant notions and theory of categories and functors will be introduced from scratch in the lecture). Physicists and mathematicians are equally welcome to participate.If in-person classes are not an option because of the COVID-19 pandemic, lectures and exercise classes will be held online (via BigBlueButton or similar free and open software) synchronously. Optional discussion sessions will be offered on a regular basis, and questions and other feedback are encouraged also by messenger or email. Lecture notes and other supplementary material will be made availble.UPDATE (in mid-September): The course will start in on-site mode on October 11. Participants are encouraged to let the lecturer know if/when they prefer on-site or online lectures.
Assessment and permitted materials
Questions and comments during and after the lectures are encouraged, regular attendance is recommended. To get credits for this course, students will be asked to present their solutions for at least one exercise, and participate in two written tests, one in December and one at the end of the term.
Minimum requirements and assessment criteria
To formally pass this course, one exercise solution must be presented, and at least 50% of the combined maximal score in the two written tests must be obtained. The written tests will each contribute ⅓ to the final mark, the exercise presentation will contribute another ⅓.
Examination topics
Content of the lecture course and exercises.
Reading list
Association in the course directory
M-ERG
Last modified: We 14.09.2022 15:49