moduli space

A moduli space is a mathematical concept that captures all possible shapes or configurations of a particular type of object, considering two objects the same if they can be transformed into each other without tearing or gluing. Think of it as a "map" that organizes every distinct form an object can take—like all possible ways to bend or stretch a surface—so that mathematicians can study the full variety of these shapes systematically. It provides a structured framework to understand how objects of a certain class differ and relate to one another within a unified setting.