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.

Teaching (DOI)

Since 2022	Teaching at Ecole Polytechnique
03-06/ 2024-2026	Measure and Integration (FMA 3S001) (instructor)
04-06/ 2025, 2026	Analyse réelle et introduction aux méthodes variationnelles (MAT371, PC)
09-12/ 2022	Measure and Integration (MAA301) (instructor)
11/2022-02/2023	Distributions, analyse de Fourier et EDP (MAT432, PC)

2024-2025	Teaching at Sorbonne University
	M2 Mathématiques et Applications
01-03/ 2025	Analyse des effets géométriques sur les équations dispersives, (short description)

2015-2016 – Teaching (substitute) at University Nice Sophia-Antipolis

Analyse de Hilbert (M1) — 36H (teaching assistant)
Preparation for the admission to Superior Schools -20H (instructor)

2011-2015 – Teaching (substitute) at University Nice Sophia-Antipolis

2012-2013 Master course (M2) : “Wave equation in domains with boundary” — 15H (instructor)
Integration and Probability (L3 MASS) — 40 H/ year (TA)
Preparation for the admission to Superior Schools –20H/ year (instructor)

2009-2010 – Teaching at Johns Hopkins University, Baltimore MD

Linear Algebra (Math. 201) (180 students) — 50H (instructor)
Differential Equations with Applications (Math. 302) — 70H (instructor)
Introduction to Real Analysis (Math. 405) — 30H (instructor)
Topics in Analysis (Math. 726) – (graduate course) – 40H (instructor)

2006-2009 – Teaching Assistant at Paris 11 University (Orsay)

Calculus (Math. 151 and Math.152) (67,5 H / year – instructor and TA)