ERC Starting grant – Waves propagation in real life physics occur in media which are neither homogeneous or spatially infinity. The birth of radar/sonar technologies (and the raise of computed tomography) greatly motivated numerous developments in microlocal analysis and the linear theory. Only recently toy nonlinear models have been studied on a curved background, sometimes compact or rough. Understanding how to extend such tools, dealing with wave dispersion or focusing, will allow us to significantly progress in our mathematical understanding of physically relevant models. There, boundaries appear naturally and most earlier developments related to propagation of singularities in this context have limited scope with respect to crucial dispersive effects. Despite great progress over the last decade, driven by the study of quasilinear equations, our knowledge is still very limited. Going beyond this recent activity requires new tools whose development is at the heart of this proposal, including good approximate solutions going over arbitrarily large numbers of caustics, sharp pointwise bounds on Green functions, development of efficient wave packets methods, quantitative refinements of propagation of singularities (with direct applications in control theory), only to name a few important ones.

CV

SITUATION PROFESSIONNELLE

2023– Membre senior de l’Institut universitaire de France

2019– Professeur, Institut de Mathématiques de Jussieu (IMJ-PRG), Sorbonne Université

2011-2016 Membre junior de l’Institut universitaire de France

2010-2019 Professeur, Laboratoire Jean-Alexandre Dieudonné , Université Côte d’Azur

2002-2010 Professeur, Laboratoire Analyse, Géométrie et Applications, Université Paris 13

1998-2002 Chargé de recherche, Laboratoire d’Analyse Numérique, CNRS et Université Pierre et Marie Curie

1996-1998 Visiting Research Fellow, Department of Mathematics,

Program in Applied and Computational Mathematics, Princeton University

FORMATION

2001 : Habilitation à diriger la recherche, Laboratoire d’Analyse Numérique, CNRS et Université Pierre et Marie Curie

1996 : Thèse de Doctorat, Centre de Mathématiques, Ecole Polytechnique