In physical sciences, exact values are oftentimes difficult—in some cases, impossible—to obtain and approximate values are
observed and utilized instead. It is thus important to know whether a quantify under study remains stable when other parameters are slightly

perturbed. In this talk, we will discuss stability of the spectrum of the complex Neumann Laplacian when the underlying analytic and geometric

structures change. This talk is based on the joint work with Weixia Zhu.