89 citations · 1.1k across the 43 of their papers we have counts for
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Sharp polynomial bounds on the number of Pollicott-Ruelle resonances
Kiril Datchev, Semyon Dyatlov, Maciej Zworski
We give a sharp polynomial bound on the number of Pollicott-Ruelle resonances. These resonances, which are complex numbers in the lower half-plane, appear in expansions of correlat…
Fractal Weyl laws for asymptotically hyperbolic manifolds
Kiril Datchev, Semyon Dyatlov
For asymptotically hyperbolic manifolds with hyperbolic trapped sets we prove a fractal upper bound on the number of resonances near the essential spectrum, with power determined b…
Scattering phase asymptotics with fractal remainders
Semyon Dyatlov, Colin Guillarmou
For a Riemannian manifold which is isometric to the Euclidean space outside of a compact set, and whose trapped set has Liouville measure zero, we prove Weyl type asymptoti…
Microlocal limits of plane waves and Eisenstein functions
Semyon Dyatlov, Colin Guillarmou
We study microlocal limits of plane waves on noncompact Riemannian manifolds (M,g) which are either Euclidean or asymptotically hyperbolic with curvature -1 near infinity. The plan…
Quantum ergodicity for restrictions to hypersurfaces
Semyon Dyatlov, Maciej Zworski
Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is…