MS Seminar (Mathematics - String Theory)

Speaker: Minyoung You (APCTP, Pohang)
Title: Congruence representations of SL_2(Z) and their physical uses
Date (JST): Tue, Oct 25, 2022, 13:30 - 15:00
Place: Hybrid
Abstract: It is well-known that the modular data of rational conformal field theories (RCFTs) or modular tensor categories (MTCs) form (projective) representations of SL_2(Z). In fact, it turns out that these representations belong to a special class of representations, called congruence representations. I will give an introduction to congruence representations of SL_2(Z) and their application to the classification of RCFTs and MTCs. I will also discuss the generalization to fermionic theories, which involves congruence representations of the theta subgroup of SL_2(Z), and present a classification of fermionic topological orders of rank 10.