Towards Lax formulation of integrable hierarchies of topological type

The Givental group action on a product of several copies of KdV tau functions produces a new tau function that satisfies the Givental–Milanov Hirota Quadratic Equation. We calculate its Lie algebra action and thus obtain deformations of Lax and Sato–Wilson equations. In particular we show that this produces the KdV deformation formulas of Buryak, Posthuma and Shadrin in the Dubrovin–Zhang Hamiltonian approach. We see this as a first step towards a Lax formulation of integrable hierarchies of topological type.
This talk is based on joined work with Guido Carlet, Hessel Posthuma and Sergey Shadrin.