Fusion Categories and Low-dimensional TQFT
Berkeley, Fall 2020. CCN: 15455 (20)
Lecture Schedule (on Zoom, Fridays, 3:10–4:30 pm)
(2:40–4:00 pm starting 11/13)
- 9/4: Constantin Teleman, Overview and goals of the seminar
- 9/11: Constantin Teleman, Overview 2: (Higher) algebraic structures
and (lower) TQFTs [11, §2, 3]
- 9/18: Jeremy Taylor, Kronecker-Weber theorem and Class Field theory
Special time: 10:40–12
- 9/25: Claudia Scheimbauer: Higher categories, definitions and
examples [1, 9, 10]
Special time: 10:40–12
Two Closely related lectures at MSRI
- 10/2: Kiran Luecke, Symmetry, symmetric monoidal structures, relation to spectra
[2,9,13]
- 10/9: Kiran Luecke, Cobordism Hypothesis and TQFTs [8, 11]
- 10/16: John Nolan, Internal duals. Fusion categories I
[4, 6, 7, 12]
- 10/23: Kabir Kapoor, Fusion categories II
- 10/30: Daniel Chupin, Dualizability of Fusion
Categories. Turaev-Viro TQFT [3,5]
- 11/6: C Teleman, Examples and counterexamples
- Change of time to 2:40-4:00pm
- 11/13: Kabir Kapoor, Braided and Modular tensor categories. Witt group [3, 4]
Notes,
Equivariantization
- 11/20: C Teleman: Super-categories. Tensor, braided and symmetric
tensor structures.
- 11/25: Reshetikhin-Turaev theories. [3]
- 12/4: C Teleman, Algebraic extension of the 3-category of Fusion
Cats. Wales seminar slides""
Bibliography:
- Barrett, Meusburger, Schaumann: Gray
categories with duals..., §2
- Bousfield and Friedlander:
Segal Gamma-spaces
- Brochier, Jordan, Snyder: Dualizability of
braided tensor categories
- Davydov, Mueger, Nykshich, Ostrik: The Witt
group of braided fusion categories
- Douglas, Schommer-pries, Snyder: Dualizable
Tensor Categories
- Etingof, Gelaki, Nikshych, Ostrik: Tensor Categories, Ch.9, AMS Surveys&Monographs
- Etingof, Nykshich, Ostrik:
On Fusion Categories
- Freed: on the cobordism hypothesis
- Groth: Short course on categories
- Teichner:
Higher catgories in a nutshell
- Teleman: Five Lectures on Topological Field Theory, mind
the errata
- Teleman: Notes on fusion categories and their modules link coming soon
- Thomason: Symmetric
monoidal categories ...