My research brings the powerful tools of topology to bear on fascinating objects such as moduli spaces from algebraic geometry. The tools of one field illuminate the creations of another, and a better understanding of the structure of moduli spaces leads to results in many mathematical fields, such as number theory and even theoretical physics. It is an example of the interconnectedness of the mathematical universe. The novelty and advantage of using topological tools is that topology is designed to organise and filter information; it ignores the the local structure and sees only the underlying global structure. This allows a flexibility of models that can reveal patterns and properties that were previously invisible.