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.
Lecturer
Date
23rd September ~ 16th December, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 13:30 - 16:55 | A3-3-301 | ZOOM 03 | 242 742 6089 | BIMSA |
Prerequisite
Basic algebra and algebraic topology
Reference
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
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
Audience
Advanced Undergraduate
, Graduate
, Postdoc
Video Public
No
Notes Public
No
Language
Chinese
Lecturer Intro
Yilong Wang graduated from The Ohio State University in 2018. After working in Louisiana State University as a postdoc researcher, he joined BIMSA as an assistant research fellow in 2021. His research interests include modular tensor categories and topological quantum field theories.