The model surface method: a new step

There were several steps of construction of the model surface method. At the beginning, H. Poincare used as a model surface the 3-dimensional sphere, then J. Moser used hyperquadrics. Further appeared quadrics of higher codimension, then totally nondegenerate model surfaces were introduced. In 2020, the theory made the next step: model surfaces of an arbitrary Bloom-Graham type were considered. This was crucial for the general appearance of the theory and stated many new questions.