W-constraints in Singularity Theory

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We constructed a vertex algebra representation via the period map in singularity theory that can be used to characterize the correlation functions of a certain class of Quantum Field Theories. In particular, the main goal of the proposal was achieved for simple singularities. The 2nd major achievement is the discovery that the correlation functions satisfy an Eynard-Orantin recursion. In particular, I managed to prove a conjecture of Givental about the analyticity of the total ancestor potential in singularity theory. Understanding the relation between the vertex algebra representation and the Eynard-Orantin recursion seems to be a very interesting problem that could bring a new insight on the representation theory of W-algebras.