Student AG Seminar: The moduli space of semistable vector bundles of fixed rank and determinant on g

The moduli space of semistable vector bundles of fixed rank and determinant on curves has been studied extensively since the 1960s. It has been proven to admit a moduli space by Mumford, Newstead via GIT, and to admit a good moduli space by Alper. The construction of specific ones is due to Narasimhan, Ramanan, Drezet, Beauville, etc.  And the moduli space of semistable twisted vector bundles was constructed and studied by Lieblich, Yoshioka, Caldaradu in the early 2000. In this ongoing project, we construct and compute the moduli space of semistable vector bundles on gerbes of certain rank and determinant and tie them to the classical constructions stated above.