Data: 13/07/2016
Hora: 15:30h
Local: C119

Palestrante: Reimundo Heluani (IMPA) 

Título: Special holonomy and representation theory of vertex algebras 

Resumo: To any smooth manifold M one can attach a vertex operator superalgebra V in a canonical way. When M has special holonomy the character of V is expected to have special modular properties, for example, if M is Calabi-Yau, the character of V is a weak Jacobi form. Also in the case when M has special holonomy, V admits commuting embeddings of certain special W algebras. The characters of representations of W turn out not to be modular but rather mock modular forms. When one decomposes the character of V in terms of characters of W, the generating sequence, besides being Mock modular itself for trivial reasons, shows some striking connections with the theory of finite simple groups. We will describe the situation in the case when M is a K3 surface, which after an observation of Eguchi, Ooguri and Tachikawa is expected to have connections with Mathieu's M24 group as well as give some speculations as to what may happen in the other special holonomy cases.