Geometric and categorical aspects of CFTs

Objectives

1) To discuss the interrelations between the algebraic approaches, specifically vertex operator algebras and their representation theory, and the geometric approaches to two-dimensional conformal field theories.
2) To relate certain constructions relevant to low-dimensional topological quantum field theories, specifically modular functors, cohomological field theories}, topological recursion and factorisation homology, in which axioms involving the degeneration or glueing of surfaces play a prominent role, in order to disseminate mathematical techniques between communities.