Quantization of bialgebras via factorization cohomology

We will discuss an approach to deformation quantization of Lie bialgebras similar to Kontsevich/Tamarkin formality for quantization of Poisson manifolds.
The idea is to prove that  deformation complex of (homotopy, conilpotent) dg-bialgebras B is equivalent to the deformation complex of a functorial little disk
algebra associated to B. This later complex is factorization cohomology (or higher Hochschild cohomology) and has a homotopy Lie algebra structure given
by Deligne conjecture which controls the quantization and can be studied explicitly in certain important cases. This is joint work with Sinan Yalin.