Research areas.
PDE, differential geometry, spectral theory.
Current research interests.
Geometric scattering theory, microlocal analysis (resolvents,
Eisenstein functions and distorted plane waves, scattering operators) 
Conformal geometry (FeffermanGraham program, AdSCFT) 
Hyperbolic geometry and Teichmüller theory (geometrically finite
hyperbolic 3manifolds, renormalized volume and ChernSimons
invariants) 
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 noncompact settings, Ruelle resonances for flows,
cohomological equations) 
Inverse
problems, analytic (Calderon problem, spetcral rigidity) and
geometric (Xray 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) 
Publications
and preprints
Vita
Collaborators
Pics
Links
CONFERENCES :
Winter school : Resonances: scattering and dynamics, 2123 february 2017, Orsay.
Resonances: Geometric Scattering and Dynamics, 1317 March 2017, CIRM Luminy.
LMS/CLAY Summer School in Cardiff, 2630 june 2017.
