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

• B. Pineau, J. P. Ramos, M. Taylor, "Phase retrieval for Schrödinger evolutions". Preprint at arXiv:2609.30511.
• C. Biswas, E. Carneiro, T. Flock, J. Madrid, D. Oliveira e Silva, B. Stovall, J. Tautges, "Sharp endpoint extension inequalities for the moment curve on finite fields II: an extremal property of the uniform distribution". Preprint at arXiv:2609.29882.
• 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.
• A. Guerra, J. M. Machado, J. P. Ramos, "On the effective sharp stability of the Faber-Krahn inequality". Preprint at arXiv:2609.07772.
• C. Bortolotto, J. P. Ramos, "A complex-analytic proof of square-restricted stable phase retrieval in Fock space". Preprint at arXiv:2608.26365.
• H. Tavares, G. Verzini, J. Yu, "On the emergence of dead cores in elliptic systems with sublinear competitive interactions". Preprint at arXiv:2607.25943.
• J. P. Ramos, "Eigenfunctions, free boundaries, and time-frequency localization". Preprint at arXiv:2607.21590.
• B. Bruce, D. Oliveira e Silva, B. Stovall, "Existence of maximizers for Lp Fourier extension from the hyperbolic paraboloid". Preprint at arXiv:2607.13181.
• P. Abdalla, J. de Dios Pont, J. P. Ramos, M. Taylor, "Stable phase retrieval for spans of independent random variables". Preprint at arXiv:2607.06693.
• S. Bertolini, J. de Dios Pont, B. Pineau, M. Taylor, J. P. Ramos, "L2-Stability for STFT phase retrieval". Preprint at arXiv:2605.20527.
• 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.