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 .
讲师
日期
2024年04月08日 至 07月01日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一 | 13:30 - 16:55 | A3-3-301 | ZOOM 03 | 242 742 6089 | BIMSA |
修课要求
Basic notion of fusion categories.
参考资料
- 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).
听众
Graduate
视频公开
不公开
笔记公开
不公开
语言
中文
讲师介绍
王亦龙于2018年从俄亥俄州立大学数学专业博士毕业，之后在路易斯安那州立大学任博士后，并于2021年加入BIMSA任助理研究员。主要研究方向为量子代数与量子拓扑，具体课题包括模张量范畴及其对应的拓扑量子场论的代数与数论性质。