Moore-Tachikawa conjecture and chiral algebras of class S

Motivated by the string theory, Moore and Tachikawa conjectured in
2011 the existence of two-dimensional topological quantum field
theories whose values are holomorphic symplectic varieties.
Independently, motivated by the same physical background, Beem, Lemos,
Liendo, Peelaers, Rastelli and van Rees conjectured the existence of two-dimensional topological quantum field theories whose values are
vertex algebras. In my talk I will survey these conjectures and then explain how the conjecture on vertex algebras implies the conjecture on symplectic varieties.