SHADE is live. Until the end of 2028, 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 nine researchers, three students and twelve international consultants.

• Diogo Oliveira e Silva (IST/CAMGSD)
• Simão Correia (IST/CAMGSD)
• Hugo Tavares (IST/CAMGSD)
• João Pedro Ramos (IMPA)
• Giuseppe Negro (IST/CAMGSD)
• Delia Schiera (IST/CAMGSD)
• Jorge Drumond Silva (IST/CAMGSD)
• Maciej Kucharski (IST/CAMGSD)
• Giuseppe Lamberti (IST/CAMGSD)

Publications

• S. Mauro, D. Schiera, H. Tavares, "Least energy solutions for cooperative and competitive systems with Neumann boundary conditions". J. Differential Equations, 459 (2026), 114135.

Preprints

• F. Gonçalves, G. Negro, D. Oliveira e Silva, "Gaussians do not always maximize mixed-norm Strichartz inequalities for the Schrödinger equation". Preprint at arXiv:2609.11644.
• M. Kucharski, M. Kwaśnicki, "Shorter proof of dimension-free Lp estimates for maximal Riesz transforms". Preprint at arXiv:2609.11537.
• H. Tavares, G. Verzini, J. Yu, "On the emergence of dead cores in elliptic systems with sublinear competitive interactions". Preprint at arXiv:2607.25943.
• B. Bruce, D. Oliveira e Silva, B. Stovall, "Existence of maximizers for Lp Fourier extension from the hyperbolic paraboloid". Preprint at arXiv:2607.13181.
• K. Böröczky, J. M. Machado, J. P. Ramos, "Quantitative Stability for Minkowski's problem". Preprint at arXiv:2603.17726.
• M. Clapp, A. Saldaña, D. Schiera, "Sublinear elliptic equations with a sharp change of sign in the nonlinearity". Preprint at arXiv:2603.11766.
• A. Chapouto, S. Correia, J. P. Ramos, "Gauge transform for the Korteweg-de Vries equation and well-posedness below the H^{−1}-scale". Preprint at arXiv:2601.15060.
• M. Alexis, L. Becker, D. Oliveira e Silva, C. Thiele, "An SU(2n)-valued nonlinear Fourier transform". Preprint at arXiv:2601.03987.