Cohomology in algebra, geometry, physicsand statistics

Vertex algebras and foliations associated to CFT correlation functions

We recall the notion of CFT/vertex operator algebras, their modules, construction of CFT correlation functions on Riemann surfaces of various genus, and their relations to modular forms. Using properties of vertex algebra intertwining operators and characters, we show how to construct a foliation associated to a grading-restricted vertex algebra. A short synopsis of the proof for coordinate-independence of the construction will be given. Finally, we will shortly discuss cohomology and characteristic classes of grading-restricted vertex algebras and corresponding foliations.