Daniel Ioan Tataru

Specialist in the modern theory of partial differential equations. Unique continuation theorem (1995) unified previous results, showing that a metric perturbation can be recovered from the scattering matrix. Most recently (2013), with B. Haberman, showed that conductivity can be recovered from boundary measurements under mere Lipschitz regularity, largely resolving a longstanding conjecture. Extensive work on strongly nonlinear wave equations has featured the development and deployment of phase space and wave packet techniques for the analysis of solutions under optimal or nearly optimal regularity assumptions on initial data, in borderline (critical) cases. Specific results include (with H. Smith) sharp well-posedness theory for nonlinear waves, and (with Sterbenz) large data results for wave maps,-nonlinear generalizations of wave equation solutions to functions taking values on manifolds. Published a rigorous proof of Price's law (1972) about decay of waves on black hole backgrounds, recently (2012) extended (with J. Metcalfe and M. Tohaneanu) to non-stationary space-times. Proved the Threshold Conjecture for geometric nonlinear waves, namely for Wave Maps (2009) with J. Sterbenz, Maxwell-Klein Gordon (2015) and Yang Mills (2017), last two jointly with S0J. Oh. Current work on many water wave models and integrable systems.