Title：On the classification of transitive modular tensor categories

Abstract：The notion of modular (tensor) categories evolved from the study of rational conformal field theory and topological quantum field theory. It has deep connections with many areas of mathematics and physics, including the representation theory of (quantum) groups, vertex operator algebra and quantum invariants of knots/link/3-manifolds. Modular categories enjoy rich arithmetic properties such as the congruence kernel property and the Galois group action on simple objects. In this talk, we will briefly review the theory of modular categories with a focus on their arithmetic properties. Then we will present our recent work on the complete classification of modular categories which admit transitive Galois group actions.

Speaker：Yilong Wang，

Yilong Wang, graduated from Ohio State University in 2018, is currently a postdoctoral fellow at Louisiana State University. Wang is mainly engaged in the research of modular tensor category and its corresponding topological quantum field theory. His work involves the classification of modular tensor category, numerical invariants, structure of Witt group and topological quantum field theory. His papers have been published in the journals such as Selecta Mathematica, Algebraic & Geometric Topology, etc.

Date：10:30am-11:30am 2021-5-7（Friday）.

Venue: 204

Tencent Meeting ID： 939 577 898

Organizer：School of Mathematical Science

Students and teachers who are interested in number theory, tensor category and Hopf algebras are welcome.