BIMSA > From quadratic forms to modular tensor categories
From quadratic forms to modular tensor categories
In the first part of the course, we review the algebraic theory of bilinear and quadratic forms and their applications to topological problems. Then we will introduce the categorifications of these algebraic structures, namely, braided tensor categories and modular tensor categories. We will see how these categorical structures help us in the study of quantum topology in the context of topological field theories.
讲师
王亦龙
日期
2025年09月23日 至 12月16日
位置
Weekday Time Venue Online ID Password
周二 13:30 - 16:55 A3-3-301 ZOOM 03 242 742 6089 BIMSA
修课要求
Basic algebra and algebraic topology
参考资料
W. Scharlau, Quadratic and Hermitian Forms
J. Milnor and D. Husemoller, Symmetric Bilinear Forms
B. Bakalov and A. Kirillov Jr., Lectures on Tensor Categories and Modular Functors
V. Turaev, Quantum Invariants of Knots and 3-Manifolds
听众
Advanced Undergraduate , Graduate , 博士后
视频公开
不公开
笔记公开
不公开
语言
中文
讲师介绍
王亦龙于2018年从俄亥俄州立大学数学专业博士毕业，之后在路易斯安那州立大学任博士后，并于2021年加入BIMSA任助理研究员。主要研究方向为量子代数与量子拓扑，具体课题包括模张量范畴及其对应的拓扑量子场论的代数与数论性质。