Universität Wien
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260093 VU Topological quantum field theory 3 (2021W)

7.00 ECTS (4.00 SWS), SPL 26 - Physik
Prüfungsimmanente Lehrveranstaltung
VOR-ORT
Moodle

An/Abmeldung

Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").

Details

max. 15 Teilnehmer*innen
Sprache: Englisch

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

  • Donnerstag 07.10. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Dienstag 12.10. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Donnerstag 14.10. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Dienstag 19.10. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Donnerstag 21.10. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Donnerstag 28.10. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Donnerstag 04.11. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Dienstag 09.11. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Donnerstag 11.11. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Dienstag 16.11. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Donnerstag 18.11. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Dienstag 23.11. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Donnerstag 25.11. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Dienstag 30.11. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Donnerstag 02.12. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Dienstag 07.12. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Donnerstag 09.12. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Dienstag 14.12. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Donnerstag 16.12. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Dienstag 11.01. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Donnerstag 13.01. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien
  • Dienstag 18.01. 12:15 - 13:45 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Donnerstag 20.01. 09:00 - 10:30 Kurt-Gödel-Hörsaal, Boltzmanngasse 5, EG, 1090 Wien

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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.

Art der Leistungskontrolle und erlaubte Hilfsmittel

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.

Mindestanforderungen und Beurteilungsmaßstab

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.

Prüfungsstoff

Content of the lecture course and exercises.

Literatur

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

Zuordnung im Vorlesungsverzeichnis

M-ERG

Letzte Änderung: Mo 22.11.2021 18:29