Topological recursion and its ramifications

Topological recursion is a universal procedure that helps 
building connections among enumerative geometry, complex geometry, 
intersection theory and integrability. It associates to some initial 
data called spectral curve, consisting of a Riemann surface and some 
extra data, a doubly indexed family of differentials on the curve, which 
often encode interesting enumerative geometric information, such as 
volumes of moduli spaces, matrix model correlation functions and 
intersection numbers. In this talk I will provide an introduction to 
this rich domain, finishing with an overview of the exciting 
developments in the field.