Universität Wien

260003 VU Factorisation algebras in field theory (2025W)

5.00 ECTS (3.00 SWS), SPL 26 - Physik
Continuous assessment of course work
Moodle
Th 11.12. 15:00-17:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien

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 09.10. 15:00 - 17:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 16.10. 15:00 - 17:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 23.10. 15:00 - 17:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 30.10. 15:00 - 17:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 06.11. 15:00 - 17:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 13.11. 15:00 - 17:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 20.11. 15:00 - 17:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 27.11. 15:00 - 17:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 04.12. 15:00 - 17:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 18.12. 15:00 - 17:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 08.01. 15:00 - 17:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 15.01. 15:00 - 17:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 22.01. 15:00 - 17:30 Kleiner Seminarraum, Zi.3510, Boltzmanngasse 5, 5. Stk., 1090 Wien

Information

Aims, contents and method of the course

This course is focused on certain applications of category theory in mathematical physics. We will study an approach to observable algebras in the Batalin-Vilkovisky formalism for gauge theories via factorisation algebras. Factorisation algebras are certain cosheaves on topological spaces which are apt to model observable algebras in euclidean signature. Along the way, we will introduce the necessary notions from homological algebra as well as the functor-of-points perspective from algebraic geometry in order to motivate the reformulation of perturbative field theory as the study of formal moduli problems. Some essential examples such as scalar field theory, Yang-Mills theory, and Chern-Simons theory will be treated in this context. This will lead up to a discussion of some open problems in the area.

Prerequisites: Familiarity with basic algebra, basic point-set topology, basic category theory, and basic manifold theory. Familiarity with gauge theories is advantageous but not necessary. We will recall the necessary material depending on need.

The course is aimed at physicists and mathematicians in equal measure.

Assessment and permitted materials

We will discuss exercises together in class. Participation in these discussions is integral to the course; submission of solutions is otherwise not necessary.

Evaluation will be based on one short written midterm test in late November and one oral test at the end of the term.

Minimum requirements and assessment criteria

In order to pass the course, students must pass both tests by obtaining at least 40% of the total points in each test. The grade in the midterm test will contribute 40% and the grade in the oral test will contribute 60% to the final grade.

Examination topics

Content of the course and the exercises discussed in class.

Reading list

K. Costello and O. Gwilliam, "Factorization Algebras in Quantum Field Theory", Volumes 1 and 2.
G. Ginot, "Notes on Factorization Algebras, Factorization Homology and Applications"

Association in the course directory

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

Last modified: Fr 10.10.2025 12:47