The conference will make an overview of the state of the art in a rapidly developing area of analysis concerned with application of the techniques of operator theory to the asymptotic analysis of parameter-dependent differential equations and boundary-value problems. From the physical point of view, the parameter normally represents a length-scale in the situation modelled by the equation: for example, a wavelength in wave propagation, or the inhomogeneity size in the theory of periodic composites. The theory of linear operators in a Hilbert space (symmetric, self-adjoint, dissipative, non-selfadjoint), which has enjoyed several decades of outstanding progress, had been, for much of its time, restricted to abstract analysis of general classes of operators, accompanied by ad-hoc examples and applications to perturbations of the Laplace operator. The meeting is aimed at making a step-change in re-assessing the existing body of knowledge in the related areas, as a modern operator-theoretic version of the classical asymptotic analysis. This will generate new research directions in the asymptotic study of operator families, where the abstract and applied streams are aligned with each other.