Differential operators approach to Khovanov–Rozansky calculus

For Khovanov–Rozansky cohomologies, we develop a construction of differential operators in odd variables, associated with all link diagrams, including tangles with open ends. These operators become nilpotent only for diagram with no external legs, but even for open tangles one can develop a factorization formalism, which preserve Reidemeister/topological invariance – the symmetry of the problem. During this talk, I am going to introduce our approach, consider relations which allows one to simplify calculations of the Khovanov–Rozansky polynomials and provide examples.