On braided fusion categories
This course closely examines the material in [DGNO10]. We begin by providing a thorough and self-contained overview of the known results on braided fusion categories, without assuming they are pre-modular or non-degenerate. Following this, the primary objective of this course is to introduce the concept of the core of a braided fusion category. This concept enables us to distinguish the components of a braided fusion category that are not derived from finite groups.
Lecturer
Date
13th March ~ 12th June, 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], and [IV] 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.
Links to the relevant previous courses:
[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.
Links to the relevant previous courses:
[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...