Non Gaussian Minkowski functionals and extrema counts for 2D sky maps
  In the conference presentation we have reviewed the theory of non-Gaussian
geometrical measures for the 3D Cosmic Web of the matter distribution in the
Universe and 2D sky data, such as Cosmic Microwave Background (CMB) maps that
was developed in a series of our papers. The theory leverages symmetry of
isotropic statistics such as Minkowski functionals and extrema counts to
develop post- Gaussian expansion of the statistics in orthogonal polynomials of
invariant descriptors of the field, its first and second derivatives. The
application of the approach to 2D fields defined on a spherical sky was
suggested, but never rigorously developed. In this paper we present such
development treating effects of the curvature and finiteness of the spherical
space $S_2$ exactly, without relying on the flat-sky approximation. We present
Minkowski functionals, including Euler characteristic and extrema counts to the
first non-Gaussian correction, suitable for weakly non-Gaussian fields on a
sphere, of which CMB is the prime example.
