SHADE will be live for three years staring on December 22nd, 2025. It will address central open problems at the interface of harmonic analysis, dispersive and elliptic PDE, from sharp restriction theory, constructive stability and sharp regularity thresholds to blowup and singular analysis. The team consists of seven researchers who will be joined by two postdocs, three students and twelve international consultants. Supported by Fundação para a Ciência e Tecnologia, project with reference 2023.17881.ICDT, with DOI identifier (TBA).