The theory and applications of interferometric constants to astronomical measurements

In an interferometer composed of N>=3 elements, there are certain quantities that are invariant under local corruption factors like the medium of propagation and the instrument itself. I will describe this concept from the context of radio interferometry, and provide a prescription for determining the complete and independent set of invariants using 3-element closed loops as fundamental units while unifying different descriptions for various classes of these invariants. I will also highlight some of their key astronomical applications, including the inference of morphological parameters of the supermassive black holes at the centres of M87 and the Milky Way using planet-scale Very Long Baseline Interferometry, and in observational cosmology using redshifted 21 cm line to detect the formation of large-scale structures in the high-redshift Universe.