Modularity in vertex operator algebras

開催日時: 
2018/06/27 Wed 16:30 - 17:30
場所: 
RIMS110号室
講演者: 
Chongying Dong
講演者所属: 
京大・数理研 & University of California, Santa Cruz
概要: 

Modular invariance of characters of a rational conformal field theory has been known since the work of Cardy. It was proved by Zhu that the the space spanned by the irreducible characters of a rational vertex operator algebras is a representation of the full modular group. This representation is a powerful tool in the study of vertex operator algebras and conformal field theory. It conceives many intriguing arithmetic properties, and the Verlinde formula is certainly a notable example. It has been conjectured my people that the kernel of this representation is a congruence subgroup, or the irreducible characters are modular functions on a congruence subgroup. This expository talk will survey our recent proof of this conjecture.