Dmitri Pavlov's Lectures on Functorial Field Theory

This is an online Zoom class on functorial field theory. Meeting ID: 963 0871 5590. For password, email me or ask one of the participants.

The initial goal is to understand the statement of the geometric cobordism hypothesis, including the relevant background material in homotopy theory. Additional goals include constructing elementary examples of functorial field theories using GCH. Further goals include looking at more advanced examples, including geometric factorization homology.

Time: Sunday, 15:00–17:00 UTC. (Remember to convert to your time zone.)

Handwritten lecture notes.

Lecture 1: Sunday, October 15. Introduction. Video.

Lecture 2: Sunday, October 22. Functor of points: smooth sets. Video.

Lecture 3: Sunday, November 5. Functor of points: smooth sets, C^∞-rings. Video.

Lecture 4: Sunday, November 12. Functor of points: C^∞-rings. Video.

Lecture 5: Sunday, November 19. Sheaves. Video.

Lecture 6: Sunday, November 26. Stacks. Video.

Lecture 7: Sunday, December 3. Čech nerves and cocycle data.


Preliminary syllabus

Homotopy theory

Higher category theory

Smooth bordism categories

Locality and codescent

The geometric cobordism hypothesis


Additional sources

Stephan Stolz, Peter Teichner. Supersymmetric field theories and generalized cohomology.

Stephan Stolz, Peter Teichner. What is an elliptic object?

Henning Hohnhold, Matthias Kreck, Stephan Stolz, Peter Teichner. Differential forms and 0-dimensional super symmetric field theories.

Henning Hohnhold, Stephan Stolz, Peter Teichner. From minimal geodesics to supersymmetric field theories.

Daniel Berwick-Evans.

Elke Market. Field theory configuration spaces for connective ko-theory.

Corbett Redden. String structures and canonical 3-forms.

Florin Dumitrescu.

Peter Teichner. Elliptic cohomology via conformal field theory. (Lecture notes for a 2007 class at Berkeley.)

Fei Han. Supersymmetric QFT, Super Loop Spaces and Bismut-Chern Character.

Stephan Stolz, Peter Teichner. Traces in monoidal categories.