The universal moduli space M(G) can be constructed over M_g. The goal of the present project is to construct a compactification of M(G) over $\bar{M}_g$. In other words, we wish to give a universal construction over $\bar{M}_g$ for all groups G, with singularities which are simple.
Source
Source
Science and Engineering Research Board (SERB), DST 2022-23