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.

Students

Post-doctoral students

Jingrui NIU	2021 – 2023	ERC ANADEL

Felice IANDOLI	2018 – 2022	ERC ANADEL
_{F.Iandoli is now junior researcher at Univ. of Calabria.}
Lucrezia COSSETTI	2018	ANR ANADEL
_{L.Cossetti is now a postdoc fellow at KIT, Karlshure.}
Jiqiang ZHENG	2017 – 2018	ANR ANADEL
_{J.Zheng is now junior researcher at IAPCM, Pékin.}

PhD Students

Len MEAS	2014 – 2017	ERC SCAPDE
_{L.Meas is now at the Royal Univ. of Phnom – Penh,}	_Cambodge

This PhD thesis has been co-directed with Gilles Lebeau at LJAD, Nice.

Master Students

3 master students (one M2 thesis (2018) ; two M1 thesis (2014, 2021))

Member of the jury for the PhD defense of

Jingrui NIU (2021), Chenmin SUN (2018), David LAFONTAINE (2018)