Universität Wien

260093 VU Topological quantum field theory 3 (2021W)

7.00 ECTS (4.00 SWS), SPL 26 - Physik
Continuous assessment of course work
ON-SITE
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 07.10. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 12.10. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 14.10. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 19.10. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 21.10. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 28.10. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Thursday 04.11. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 09.11. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 11.11. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 16.11. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 18.11. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 23.11. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 25.11. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 30.11. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 02.12. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 07.12. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 09.12. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 14.12. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 16.12. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 11.01. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 13.01. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Tuesday 18.01. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 20.01. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien

Information

Aims, contents and method of the course

This course is a continuation of the introduction to an axiomatic, functorial approach to topological quantum field theory (TQFT) of the previous two terms. However, familiarity with only the basic notions and results is needed for this course (roughly only half of the previous parts: rigid monoidal categories, string diagram calculus, classifications of 1- and 2-dimensional closed TQFTs, some examples). New participants will also be provided a set of written lecture notes for the previous courses. (If students express interest via email, optional review sessions will be offered before the start of the course in early October.)

The first part of the course will introduce the notion of defect TQFTs. Very roughly, they can be thought of as the interaction of higher-dimensional closed TQFTs via lower-dimensional TQFTs; symmetries and dualities (such as mirror symmetry, S-duality, or order/disorder duality) are examples of "defects". Physically, they include boundary conditions and domain walls between different closed TQFTs, or "phases". Mathematically, defect TQFTs are defined as functors on categories of bordisms which are decomposed into decorated submanifolds, and described in terms of higher categories. The course will explain this broadly in general and thoroughly in the 2-dimensional case, partly based on the lecture notes https://arxiv.org/abs/1607.05747 but the course will offer more details. Additionally we will study several examples, including state sum models and Landau-Ginzburg models, and describe various applications.

Depending on the preferences of the audience, later parts of the course could cover 3-dimensional gauge theories of Chern-Simons type, and more generally Reshetikhin-Turaev models. Alternatively, we could focus on particularly "local" theories, so-called extended TQFTs, which are higher functors between higher categories.

Optional discussion sessions will be offered on a regular basis, and questions and other feedback are encouraged also via other channels, including anonymously via Moodle. To facilitate exchanges among themselves during the COVID-19 pandemic, an online conference room exclusively for the students (without the lecturer present) will be set up.

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Depending on the status of the pandemic, the course will be held on-site, online, or in hybrid form. Currently (mid-September) it is scheduled to be on-site. Interested students are encouraged to tell the lecturer about their preferences and/or constraints via email or via the anonymous feedback option on the course's Moodle page.

Update in November: for the foreseeable future the course will take place online.

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 (1) work out one of the exercises in written form, (2) present a solution to another exercise in class, and to (3) participate in one written test at the end of the term. We will clearly formulate guidelines on how to present solutions in written and spoken form, and the lecturer will be available for consultations when solving the exercises.

Minimum requirements and assessment criteria

Each of the requirements (1), (2) and (3) above 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

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

Last modified: Mo 22.11.2021 18:29