Triangular Prism Equations and Categorification
This course introduces to the pictorial reformulation of the Pentagon Equations (of a monoidal category) called Triangular Prism Equations, and apply it to the classification program of simple integral fusion categories, but also multiplicity-free or near-group fusion categories.
日期
2023年10月12日 至 2024年01月05日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周四,周五 | 15:20 - 16:55 | A3-2-303 | ZOOM 05 | 293 812 9202 | BIMSA |
修课要求
Be a bit familiar with the notion of monoidal category. Otherwise, consider the review part beginning the last semester course (videos and slides are available at https://bimsa.net/activity/fuscatIV ) and EGNO book in reference.
参考资料
- P. Etingof, S. Gelaki, D. Nikshych, V. Ostrik. Tensor categories. Mathematical Surveys and Monographs, 205 (2015), xvi+343pp. http://www-math.mit.edu/~etingof/egnobookfinal.pdf
- Z. Liu, S. Palcoux, Y. Ren, Triangular prism equations and categorification, arXiv:2203.06522, 33 pages, under review.
- Z. Liu, S. Palcoux, Y. Ren, Interpolated family of non group-like simple integral fusion rings of Lie type (with Zhengwei Liu and Yunxiang Ren), Internat. J. Math. 34 (2023), no. 6, Paper No. 2350030, 51 pp.
- Z. Liu, S. Palcoux, Y. Ren, Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six, Lett. Math. Phys. 112 (2022), no. 3, Paper No. 54, 37 pp.
- Z. Liu, S. Palcoux, Y. Ren, Polynomial Equations for Irrational Near Group Categories, work in progress.
- Z. Liu, S. Palcoux, Y. Ren, Triangular prism equations and categorification, arXiv:2203.06522, 33 pages, under review.
- Z. Liu, S. Palcoux, Y. Ren, Interpolated family of non group-like simple integral fusion rings of Lie type (with Zhengwei Liu and Yunxiang Ren), Internat. J. Math. 34 (2023), no. 6, Paper No. 2350030, 51 pp.
- Z. Liu, S. Palcoux, Y. Ren, Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six, Lett. Math. Phys. 112 (2022), no. 3, Paper No. 54, 37 pp.
- Z. Liu, S. Palcoux, Y. Ren, Polynomial Equations for Irrational Near Group Categories, work in progress.
听众
Undergraduate
, Graduate
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
2010年，获得马赛数学研究所（I2M）博士学位；2014-2016年，在印度数学科学研究所（IMSc）做博士后研究；2019年，在清华大学丘成桐数学科学中心（YMSC）担任为期一年的访问学者；2020-2024年，在BIMSA助理研究员 ；2024年至今，在BIMSA副研究员 。
主要研究领域包括量子代数、量子对称性、子因子、平面代数和融合范畴。在《Advances in Mathematics》、《Quantum Topology》、《IMRN》等期刊发表过论文。
主要研究领域包括量子代数、量子对称性、子因子、平面代数和融合范畴。在《Advances in Mathematics》、《Quantum Topology》、《IMRN》等期刊发表过论文。