AGM / Département mathématiques

UMR CNRS 8088

2 av. Adolphe Chauvin

95302 Cergy-Pontoise Cedex

France

I am interested in the behaviour of solutions of the wave and Schrödinger equations in chaotic environments. I try to understand to what extent these solutions present characteristics of delocalisation and randomness. The quantum ergodicity phenomenon is an example of delocalisation of these solutions when the underlying dynamics are ergodic. My research covers different types of geometry: discrete and continuous. The behaviour of waves is closely related to the geometry of the surface, space or network on which they evolve. Understanding these interactions is one of my main goals.

*Quantum ergodicity for Eisenstein series on hyperbolic surfaces of large genus*,

with Tuomas Sahlsten, Preprint.*Short geodesic loops and L*,^{p}norms of eigenfunctions on large genus random surfaces

with Clifford Gilmore, Tuomas Sahlsten and Joe Thomas, to appear in Geom. Funct. Anal. (GAFA).*Eigenfunctions and random waves in the Benjamini-Schramm limit*,

with Miklos Abert and Nicolas Bergeron, Preprint.*L*,^{p}norms and support of eigenfunctions on graphs

with Mostafa Sabri, Commun. Math. Phys. 374 (2020), 211–240.*L*,^{p}norms of eigenfunctions on regular graphs and on the sphere

with Shimon Brooks, Int. Math. Res. Not. IMRN 11 (2020), 3201–3228.*Quantum ergodicity and Benjamini-Schramm convergence of hyperbolic surfaces*,

with Tuomas Sahlsten, Duke Math. J. 166 (2017), no. 18, 3425-3460.*Quantum ergodicity and averaging operators on the sphere*,

with Shimon Brooks and Elon Lindenstrauss, Int. Math. Res. Not. IMRN 19 (2016), 6034-6064.*Quantum ergodicity on large regular graphs*,

with Nalini Anantharaman, Duke Math. J. 164 (2015), no. 4, 723–765.*Pseudo-differential calculus on homogeneous trees*,

Ann. Henri Poincaré 15 (2014), no. 9, 1697–1732.