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.
Lecturer
Date
12th October, 2023 ~ 5th January, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Thursday,Friday | 15:20 - 16:55 | A3-2-303 | ZOOM 05 | 293 812 9202 | BIMSA |
Prerequisite
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.
Reference
- 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.
Audience
Undergraduate
, Graduate
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
2010, obtained a doctorate from Institut de Mathématiques de Marseille (I2M); 2014-2016, Postdoc in Institute of Mathematical Sciences (IMSc); 2019, One-year visitor at Yau Mathematical Sciences Center (YMSC), Tsinghua University; 2020-2024, Assistant Professor at BIMSA; 2024-now, Associate Professor at BIMSA.
Main Research Fields include Quantum Algebra, Quantum Symmetry, Subfactor, Planar Algebra and Fusion Category.
Published papers in the journals Advances in Mathematics, Quantum Topology, IMRN, etc...
Main Research Fields include Quantum Algebra, Quantum Symmetry, Subfactor, Planar Algebra and Fusion Category.
Published papers in the journals Advances in Mathematics, Quantum Topology, IMRN, etc...