From spectral shape optimization to inverse problems and computational graphics, applications of spectral problems are ubiquitous in science and engineering, and their approximation presents fascinating mathematical challenges. There are three important areas of mathematical activity which examine spectral problems from distinct perspectives: applications, computation and geometry, with important overlapping interests. In this workshop researchers will present the state-of-the-art at the intersection of these areas, and help shape an ambitious research agenda pushing the frontiers of this intersection