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260081 VU Topological quantum field theory (2020W)

7.00 ECTS (4.00 SWS), SPL 26 - Physik
Continuous assessment of course work

Registration/Deregistration

Details

max. 15 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

Every second Wednesday, starting on October 21, the time slot 10:45–12:15 will be used as an exercise class, to discuss and present exercises distributed the week before. The remaining 75% of time slots will be used for lectures (with discussions) and two written tests. (An additional, optional fixed time slot every week will be offered for informal discussions and questions relating to the lecture course. The times for these extra slots will be decided together at the start of the semester.)

Wednesday 07.10. 10:45 - 12:15 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Monday 12.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Wednesday 14.10. 10:45 - 12:15 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Monday 19.10. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Wednesday 21.10. 10:45 - 12:15 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Wednesday 28.10. 10:45 - 12:15 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Wednesday 04.11. 10:45 - 12:15 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Monday 09.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Wednesday 11.11. 10:45 - 12:15 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Monday 16.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Wednesday 18.11. 10:45 - 12:15 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Monday 23.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Wednesday 25.11. 10:45 - 12:15 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Monday 30.11. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Wednesday 02.12. 10:45 - 12:15 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Monday 07.12. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Wednesday 09.12. 10:45 - 12:15 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Monday 14.12. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Wednesday 16.12. 10:45 - 12:15 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Monday 11.01. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Wednesday 13.01. 10:45 - 12:15 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Monday 18.01. 09:00 - 10:30 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 1090 Wien
Wednesday 20.01. 10:45 - 12:15 Josef-Stefan-Hörsaal, Boltzmanngasse 5, 3. Stk., 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, aesthetic 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. Handouts, detailed references, videos and other supplementary material will be offered depending on the circumstances. Interested students may also occasionally contribute non-obligatory 45-minute talks (for practice, and for in-depth study of the the chosen topics), embedded into the lecture course and prepared in close collaboration with the main lecturer.

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

A detailed, annotated list of references will be provided during this course.

Association in the course directory

M-ERG, MaInt

Last modified: We 23.09.2020 14:29