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.

Funding ID

Current funding

2018-2024 Principal Investigator of the ERC Starting Grant ANADEL (1,3 M euros over 5 years; the projet has been extended for one year due to Covid 19 pandemic)

Previous funding

2017-2018 Principal Investigator of the ANR grant “Analyse des équations disperses”, funded by French ANR (120 000 euros over 18 months; ended 06/2018)

2013-2018 Permanent member of the ERC Advanced Grant SCAPDE (coordinated by Gilles Lebeau)

2012-2016 Member of the ANR grant GEODISP – “Geometry and dispersion for nonlinear waves” (coordinated by Fabrice Planchon)

2008-2011 Member of the ANR grant “EDP- Dispersives” (coordinated by Nicolas Burq)