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.
Publications
- Quantum ergodicity for Eisenstein series on
hyperbolic surfaces of large genus,
with Tuomas Sahlsten, Preprint.
- Short geodesic loops and Lp
norms of eigenfunctions on large genus random surfaces,
with Clifford Gilmore, Tuomas Sahlsten and Joe Thomas, Geom. Funct. Anal. (GAFA) 31 (2021) 62-110.
- Eigenfunctions and random waves in the Benjamini-Schramm limit,
with Miklos Abert and Nicolas Bergeron, to appear in Journal of Topology and Analysis.
- Lp norms and support of eigenfunctions on graphs,
with Mostafa Sabri,
Commun. Math. Phys. 374 (2020), 211–240.
- Lp 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.
