Prerequisite

It should be helpful to be a bit familiar with the general category theory, the finite group theory and the representation theory, but it is not necessary to follow the course.

Abstract

This is the sequel of the course "On Fusion Categories III" given last semester. It introduces to the notion fusion category, which can be seen as a representation theory of the (finite) quantum symmetries. It follows the book "Tensor Categories" mentioned in References. The notes and videos of the previous parts are available at: Part I: http://www.bimsa.cn/newsinfo/526244.html Part II: https://www.bimsa.cn/newsinfo/601271.html Part III: https://www.bimsa.cn/newsinfo/749627.html If you did not attend the previous semesters, you can still attend this one because the course will start by a review of the previous parts.

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-now, Assistant Research Fellow in 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, etc...