Topics on modular tensor categories
In this course, we first introduce the notion modular tensor categories, and briefly explain how they are related to many areas of mathematics and physics. Then we will focus on the algebraic properties of MTC, mainly from their rationality, Galois symmetry and congruence properties.
Lecturer
Date
27th March ~ 23rd May, 2023
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday | 09:50 - 12:15 | A3-3-201 | ZOOM 03 | 242 742 6089 | BIMSA |
| Tuesday | 19:20 - 21:45 | A3-3-201 | ZOOM 03 | 242 742 6089 | BIMSA |
Prerequisite
Graduate level algebra.
Syllabus
1. Monoidal categories
2. Braided fusion categories
3. Modular tensor categories
4. Frobenius-Schur indicator and congruence property
5. Galois symmetry and rationality
2. Braided fusion categories
3. Modular tensor categories
4. Frobenius-Schur indicator and congruence property
5. Galois symmetry and rationality
Reference
1. Etingof, Pavel; Gelaki, Shlomo; Nikshych, Dmitri; Ostrik, Victor Tensor categories. Mathematical Surveys and Monographs, 205. American Mathematical Society, Providence, RI, 2015.
2. Ng, Siu-Hung; Schauenburg, Peter Congruence subgroups and generalized Frobenius-Schur indicators. Comm. Math. Phys. 300 (2010), no. 1, 1–46.
3. Dong, Chongying; Lin, Xingjun; Ng, Siu-Hung Congruence property in conformal field theory. Algebra Number Theory 9 (2015), no. 9, 2121–2166.
2. Ng, Siu-Hung; Schauenburg, Peter Congruence subgroups and generalized Frobenius-Schur indicators. Comm. Math. Phys. 300 (2010), no. 1, 1–46.
3. Dong, Chongying; Lin, Xingjun; Ng, Siu-Hung Congruence property in conformal field theory. Algebra Number Theory 9 (2015), no. 9, 2121–2166.
Audience
Graduate
Video Public
Yes
Notes Public
Yes
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.