Title: Finding isomorphic quantum field theories     Abstract: When do two different looking quantum field theories describe the same physics? This is essentially asking when the quantum field theories are isomorphic. In the case of topological quantum field theories, there is sometimes a way to determine them via topological invariants. For a superconformal field theory, what would be the minimal set of “invariants” to determine when they are isomorphic? I will discuss some approaches to this question in the context of a particular infinite class of superconformal field theories that admit Hitchin systems. Isomorphic pairs of such theories must have the same operator contents, such as Schur index and Hall-Littlewood index. Such theories can also be described using curve configurations and this will shine light on finding pairs of isomorphic superconformal field theories, which a priori look like distinct theories. In turn, this result provides a conjecture when two theories will necessarily have the same Schur index and Hall-Littlewood index. If time permitting, I will explain how this result further sheds light on the 3d (symplectic) duality.