On braided fusion categories II
This course is a continuation of "On braided fusion categories" in [B1] and provides an in-depth exploration of the material presented in [DGNO10]. We begin with a comprehensive, self-contained overview of the key results on braided fusion categories, without assuming they are pre-modular or non-degenerate. The main focus of this course is to introduce the concept of the core of a braided fusion category, which allows us to identify the components of a braided fusion category that are not derived from finite groups.
Even if you did not attend last semester, you are welcome to join this course, as it will start with a review of the material from the previous semester.
Even if you did not attend last semester, you are welcome to join this course, as it will start with a review of the material from the previous semester.
Lecturer
Date
9th October ~ 26th December, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Thursday,Friday | 15:20 - 16:55 | A3-3-301 | ZOOM 03 | 242 742 6089 | BIMSA |
Prerequisite
Familiarity with the concept of fusion categories is assumed; however, key definitions and fundamental results will be reviewed. For further reading, please refer to [ENO05] and [EGNO15], as well as the videos and notes from the previous courses [I], [II], [III], [IV] and [B1] listed in the references.
Reference
[DGNO10] Drinfeld, Vladimir; Gelaki, Shlomo; Nikshych, Dmitri; Ostrik, Victor. On braided fusion categories. I. Selecta Math. (N.S.) 16 (2010), no. 1, 1--119.
[ENO05] Etingof, Pavel; Nikshych, Dmitri; Ostrik, Viktor. On fusion categories. Ann. of Math. (2) 162 (2005), no. 2, 581--642.
[EGNO15] Etingof, Pavel; Gelaki, Shlomo; Nikshych, Dmitri; Ostrik, Victor. Tensor categories. Mathematical Surveys and Monographs, 205. American Mathematical Society, Providence, RI, 2015. xvi+343 pp.
Link to the previous course on braided fusion categories:
[B1] http://bimsa.net/activity/BraFusCat/
Links to the previous courses on fusion categories:
[I] http://bimsa.net/activity/Fusion
[II] http://bimsa.net/activity/FusionII
[III] http://bimsa.net/activity/FusionIII
[IV] http://bimsa.net/activity/fuscatIV
[ENO05] Etingof, Pavel; Nikshych, Dmitri; Ostrik, Viktor. On fusion categories. Ann. of Math. (2) 162 (2005), no. 2, 581--642.
[EGNO15] Etingof, Pavel; Gelaki, Shlomo; Nikshych, Dmitri; Ostrik, Victor. Tensor categories. Mathematical Surveys and Monographs, 205. American Mathematical Society, Providence, RI, 2015. xvi+343 pp.
Link to the previous course on braided fusion categories:
[B1] http://bimsa.net/activity/BraFusCat/
Links to the previous courses on fusion categories:
[I] http://bimsa.net/activity/Fusion
[II] http://bimsa.net/activity/FusionII
[III] http://bimsa.net/activity/FusionIII
[IV] http://bimsa.net/activity/fuscatIV
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
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...