Universität Wien
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260024 VU 3-dimensional functorial field theories (2022S)

5.00 ECTS (3.00 SWS), SPL 26 - Physik
Continuous assessment of course work
Moodle

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).

Details

max. 15 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 10.03. 15:00 - 18:00 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 17.03. 15:00 - 18:00 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 24.03. 15:00 - 18:00 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 31.03. 15:00 - 18:00 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 07.04. 15:00 - 18:00 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 28.04. 15:00 - 18:00 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 05.05. 15:00 - 18:00 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 12.05. 15:00 - 18:00 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 19.05. 15:00 - 18:00 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 02.06. 15:00 - 18:00 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 09.06. 15:00 - 18:00 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 23.06. 15:00 - 18:00 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien

Information

Aims, contents and method of the course

This course is an introduction to examples of functorial field theories in three spacetime dimensions, meant for both theoretical physicists and mathematicians interested in the subject. After a self-contained yet steep review of the necessary tools from category theory, the first two thirds of the course will be on topological quantum field theories of Reshetikhin-Turaev type; in the last third we will study how to include spin in such theories. The course is organised jointly with Lorant Szegedy.

In physics, Reshetikhin-Turaev theories are related to the quantisation of Chern-Simons gauge theories. Mathematically the main ingredients of the theory are modular fusion categories and surgery theory, both of which will be introduced in the course. Among the applications that can be discussed are knot invariants like the Jones polynomial and the relation to 2-dimensional conformal field theory.

The course will be held in seminar style with ample room for discussions. A detailed plan, including an extended introduction and precise pointers to textbooks, will be presented in the first session. Every other session will be divided into up to 90 minutes of presentation (mostly by students) and at least 45 minutes of discussion.

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Depending on the status of the pandemic, the course will be held on-site or online. We hope and plan to be on-site, responsibly with regards to publich health. More information will be available in early March.

Assessment and permitted materials

Regular attendance and active participation are encouraged. To get credits for this course, students will be asked to give at least one presentation, and to submit a write-up of another presentation (by somebody else) or to give a second presentation.

Minimum requirements and assessment criteria

Each of the two criteria above (presentation(s) and/or write-up) will be graded individually on a scale from 1 ("very good") to 5 ("fail"), and they will equally contribute to the final grade. To formally pass the course, a final grade of 4 or better must be achieved.

Examination topics

Reading list

A detailed, annotated list of references will be provided at the beginning of the course.

Association in the course directory

M-VAF A 2, M-VAF B, M-ERG

Last modified: Th 03.03.2022 15:29