Extensions of fusion categories
In this course, we study two notions of extensions in the theory of fusion categories: graded extensions of fusion categories and modular/nondegenerate extensions of braided fusion categories. We will introduce the homotopy theory of Etingof-Nikshych-Ostrik to study the existence and classification of graded extensions of fusion categories. For modular extensions, we will first study the work of Lan-Kong-Wen on the structure of minimal modular extensions, then follow Galindo's work to connect graded extensions and modular extensions. Finally, we will briefly go over the recent solution of existence of minimal nondegenerate extensions of slightly degenerate fusion categories by Johnson-Freyd-Reutter .
Lecturer
Date
8th April ~ 1st July, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday | 13:30 - 16:55 | A3-3-301 | ZOOM 03 | 242 742 6089 | BIMSA |
Prerequisite
Basic notion of fusion categories.
Reference
- A. Davydov, M. Müger, D. Nikshych, V. Ostrik. The Witt group of non-degenerate braided fusion categories, J. Reine Angew. Math., 677, 135-177 (2013)
- V. Drinfeld, S. Gelaki, D. Nikshych, V. Ostrik. On braided fusion categories. I. Sel. Math., New Ser. 16, No. 1, 1-119 (2010).
- P. Etingof, D. Nikshych, V. Ostrik. Fusion categories and homotopy theory. Quantum Topol. 1, No. 3, 209-273 (2010).
- T. Johnson-Freyd, D. Reutter. Minimal nondegenerate extensions. J. Am. Math. Soc. 37, No. 1, 81-150 (2024).
- T. Lan, L. Kong, X.-G. Wen. Modular extensions of unitary braided fusion categories and 2+1D topological/SPT orders with symmetries. Commun. Math. Phys. 351, No. 2, 709-739 (2017).
- V. Drinfeld, S. Gelaki, D. Nikshych, V. Ostrik. On braided fusion categories. I. Sel. Math., New Ser. 16, No. 1, 1-119 (2010).
- P. Etingof, D. Nikshych, V. Ostrik. Fusion categories and homotopy theory. Quantum Topol. 1, No. 3, 209-273 (2010).
- T. Johnson-Freyd, D. Reutter. Minimal nondegenerate extensions. J. Am. Math. Soc. 37, No. 1, 81-150 (2024).
- T. Lan, L. Kong, X.-G. Wen. Modular extensions of unitary braided fusion categories and 2+1D topological/SPT orders with symmetries. Commun. Math. Phys. 351, No. 2, 709-739 (2017).
Audience
Graduate
Video Public
No
Notes Public
No
Language
Chinese
Lecturer Intro
Yilong Wang graduated from The Ohio State University in 2018. After working in Louisiana State University as a postdoc researcher, he joined BIMSA as an assistant research fellow in 2021. His research interests include modular tensor categories and topological quantum field theories.