PDE, differential geometry, spectral theory.
Current research interests.
Geometric scattering theory, microlocal analysis (resolvents,
Eisenstein functions and distorted plane waves, scattering operators) -
Conformal geometry (Fefferman-Graham program, AdS-CFT) -
Hyperbolic geometry and Teichmüller theory (geometrically finite
hyperbolic 3-manifolds, renormalized volume and Chern-Simons
Geometric and spectral invariants (determinant of Laplacians, eigenvalues, renormalized volume) -
Quantum chaos and resonances (semiclassical measures, localisation and counting resonances) -
Dynamical zeta functions and hyperbolic dynamical systems (Selberg
trace formulas in non-compact settings, Ruelle resonances for flows,
cohomological equations) -
problems, analytic (Calderon problem, spetcral rigidity) and
geometric (X-ray transform, boundary rigidity) -
Harmonic analysis (Riesz transform, multipliers, restriction theorems),
particularly in geometric settings -
Liouville gravity, random metrics on Riemann surfaces (Gaussian free
field, Gaussian multiplicative chaos, Polyakov partition function) -
Winter school : Resonances: scattering and dynamics, 21-23 february 2017, Orsay.
Resonances: Geometric Scattering and Dynamics, 13-17 March 2017, CIRM Luminy.
LMS/CLAY Summer School in Cardiff, 26-30 june 2017.