A subfactor is an inclusion of von Neumann algebras with a trivial center. Their relative size is classified by Vaughan Jones, called the Jones index, which led to the discovery of the well-known Jones Polynomial and 3-manifold invariants. Its connection between the represention theory of (quantum) groups and topological quantum field theory has been extensively studied in the past 40 years. However, subfactors beyond (quantum) group theoretical are quite rare in previous classifications. In this talk, we propose a new program to construct brand new subfactors and planar algebras, based on a surprisingly new connection between skein theory and forest graphs. It is based on joint work with Fan Lu, arXiv:2412.17790