Seminar| Institute of Mathematical Sciences
Time: Wednesday, November 18th, 2026,16:00-17:00
Location: IMS RS408
Speaker: Yilong Wang, BIMSA
Abstract: Topological field theories (TFTs) represent manifolds in vector spaces. They provide a framework where topological structures are understood algebraically and vice versa. In 3d where we live, TFTs serve as an abundant source of invariants of knots/links/3-manifolds and representations of the mapping class groups of surfaces, whose rich algbraic properties are reflected through modular tensor categories (MTCs). In this talk, we will begin with a brief overview of MTCs and the Reshetikhin‒Turaev construction of 3d-TFTs. We will then explore two key algebraic properties of MTCs: the congruence property and the Galois symmetry. Finally, we will discuss how these properties offer valuable tools for understanding the structure of MTCs and their TFTs.