On braided fusion categories - Semester 2, Session 15 скачать в хорошем качестве

On braided fusion categories - Semester 2, Session 15

This video is the recording of Session 15 (of Semester 2) of the course on braided fusion categories covering [DGNO10] in reference below. This session was given at the Beijing Institute of Mathematical Sciences and Applications (BIMSA) on 27/11/2025. Webpage: https://bimsa.net/activity/Onbrafusca... Slides and video: https://bimsa.net/doc/notes/54781.pdf https://bimsa.net/bimsavideo.html?id=... 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. Introduction 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. References [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 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