We construct a cubic cut-and-join operator description for the partition functions of all semi-simple cohomological field theories, and, more generally, for the partition functions of the Chekhov-Eynard-Orantin topological recursion on a possibly irregular local spectral curve. The cut-and-join description leads to an algebraic version of topological recursion. For the same partition functions, we also derive N families of the Virasoro constraints and prove that these constraints, supplemented by a deformed dimension constraint, imply the cut-and-join description.
The talk is based on arXiv:2202.09090.
