In this mini-course, we will explore the result of Julien Marché and Christopher-Lloyd Simon on algebraic mapping class group rigidity, along with a slight generalization given by the speaker. We begin with a brief introduction to character varieties, then shift focus to boundary theories associated with character varieties and their geometric components. Then the main focus will be on how these two perspectives—algebraic and geometric—can be successfully unified, allowing the algebraic rigidity problem reduced to the geometrical one.