Quantum Curves in the Context of Symplectic Duality

We discuss how to use the recent progress in understanding of the $x$-$y$ duality and symplectic duality in the theory of topological recursion and its generalizations in order to efficiently compute the quantum spectral curve operators for the wave functions with arbitrary base points. The paper also contains an overview of recent generalizations of the setup of topological recursion prompted by the progress in understanding the $x$-$y$ duality.