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)

  1. 9/4: Constantin Teleman, Overview and goals of the seminar
  2. 9/11: Constantin Teleman, Overview 2: (Higher) algebraic structures and (lower) TQFTs [11, §2, 3]
  3. 9/18: Jeremy Taylor, Kronecker-Weber theorem and Class Field theory Special time: 10:40–12
  4. 9/25: Claudia Scheimbauer: Higher categories, definitions and examples [1, 9, 10] Special time: 10:40–12
    Two Closely related lectures at MSRI
  5. 10/2: Kiran Luecke, Symmetry, symmetric monoidal structures, relation to spectra [2,9,13]
  6. 10/9: Kiran Luecke, Cobordism Hypothesis and TQFTs [8, 11]
  7. 10/16: John Nolan, Internal duals. Fusion categories I [4, 6, 7, 12]
  8. 10/23: Kabir Kapoor, Fusion categories II
  9. 10/30: Daniel Chupin, Dualizability of Fusion Categories. Turaev-Viro TQFT [3,5]
  10. 11/6: C Teleman, Examples and counterexamples
  11. Change of time to 2:40-4:00pm
  12. 11/13: Kabir Kapoor, Braided and Modular tensor categories. Witt group [3, 4] Notes, Equivariantization
  13. 11/20: C Teleman: Super-categories. Tensor, braided and symmetric tensor structures.
  14. 11/25: Reshetikhin-Turaev theories. [3]
  15. 12/4: C Teleman, Algebraic extension of the 3-category of Fusion Cats. Wales seminar slides""

Bibliography:

  1. Barrett, Meusburger, Schaumann: Gray categories with duals..., §2
  2. Bousfield and Friedlander: Segal Gamma-spaces
  3. Brochier, Jordan, Snyder: Dualizability of braided tensor categories
  4. Davydov, Mueger, Nykshich, Ostrik: The Witt group of braided fusion categories
  5. Douglas, Schommer-pries, Snyder: Dualizable Tensor Categories
  6. Etingof, Gelaki, Nikshych, Ostrik: Tensor Categories, Ch.9, AMS Surveys&Monographs
  7. Etingof, Nykshich, Ostrik: On Fusion Categories
  8. Freed: on the cobordism hypothesis
  9. Groth: Short course on categories
  10. Teichner: Higher catgories in a nutshell
  11. Teleman: Five Lectures on Topological Field Theory, mind the errata
  12. Teleman: Notes on fusion categories and their modules link coming soon
  13. Thomason: Symmetric monoidal categories ...