Algebraic Geometry Student's Seminar : Brauer Groups and Quotient Stacks

How nice is the structure of a stack? How close is an algebraic stack to a quotient stack? Surprisingly, in 2001, Edidin, Hassett, Kresh and Vistoli tied this question to a classical question of Brauer groups, the Br = Br' question. They showed in their paper that a gerbe is a quotient stack if and only if it comes from Azumaya algebras. In this talk, I am going to survey their work and talk about many inspirations the authors gave to the later works in the problem.