I will speak about a work in progress to prove Dubrovin conjecture about algebraic Frobenius manifolds. The conjecture is stated as follows: Semisimple irreducible algebraic Frobenius manifolds with positive degrees correspond to quasi-Coxeter conjugacy classes in irreducible Coxeter groups. Then I will explain the construction of a family of algebraic Frobenius which support the conjecture using the theory of classical W-algebras. These families are certain subvarieties in the total spaces of semiuniversal deformation of simple hypersurface singularities.