In this talk I will discuss how supersymmetric partition functions on various compact manifolds in two, three, four and five dimensions can be expressed in terms of a universal set of building blocks, the holomorphic blocks. Two and four dimensional holomorphic blocks can be reinterpreted as conformal blocks in Liouville theory via the Alday-Gaiotto-Tachikawa correspondence. I will provide a similar realisation of three and five dimensional holomorphic blocks in a q-deformed version of Liouville theory where the Virasoro algebra is replaced by the q-deformed Virasoro algebra.
