Research Interests
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Spectral geometry: study of resonances both of the Laplace-Beltrami operator and the geodesic flow
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Mathematical physics: spectral theory of chaotic, deterministic classical systems (Pollicott-Ruelle resonances) as well as complex (chaotic) quantum systems
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Harmonic analysis on Lie groups: in particular the study of wavefront sets of unitary representations
Selected publications of the working group
Higher rank quantum-classical correspondence
J. Hilgert, T. Weich, L.L. Wolf, Analysis&PDE (to appear).
Ruelle-Taylor resonaces of Anosov actions
T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, Journal of the EMS (to appear).
The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
M. Cekić, B. Delarue, S. Dyatlov, G.P. Paternain, Inventiones Mathematicae 229 (2022) 303–394.
Ruelle–Pollicott resonances for manifolds with hyperbolic cusps
Y. Guedes Bonthonneau, T. Weich, Journal of the European Mathematical Society 24 (2022) 851–923.