Fields of research
- Analysis and dynamical systems on locally homogeneous manifolds
- Discrete subgroups of Lie groups, Anosov representations
- Spectral theory
- Microlocal/semiclassical analysis
- Mathematical physics
- Oscillatory integrals in symplectic geometry and quantization
Publications
- Locally Homogeneous Axiom A Flows I: Projective Anosov Subgroups and Exponential Mixing (with Daniel Monclair and Andrew Sanders)
Geom. Funct. Anal. 35 (2025), 673–735 - Spectra of Lorentzian quasi-Fuchsian manifolds (with Colin Guillarmou and Daniel Monclair)
arXiv Preprint (2025) - Locally homogeneous Axiom A flows II: geometric structures for Anosov subgroups (with Daniel Monclair and Andrew Sanders)
arXiv Preprint (2025) - Patterson-Sullivan and Wigner distributions of convex-cocompact hyperbolic surfaces (with Guendalina Palmirotta)
arXiv Preprint (2024) - Quantum resonances and scattering poles of classical rank one locally symmetric spaces (with Joachim Hilgert)
arXiv Preprint (2024) - Resonances and weighted zeta functions for obstacle scattering via smooth models (with Philipp Schütte and Tobias Weich)
Ann. Henri Poincaré 25 (2024), 1607–1656 - Singular cohomology of symplectic quotients by circle actions and Kirwan surjectivity (with Maximilian Schmitt and Pablo Ramacher)
arXiv Preprint (2023) - A Riemann-Roch formula for singular reductions by circle actions (with Louis Ioos and Pablo Ramacher)
arXiv Preprint (2023) - The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds (with Mihajlo Cekić, Semyon Dyatlov, and Gabriel Paternain)
Invent. Math. 229 (2022), 303–394 - Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions (with Pablo Ramacher)
J. Symplectic Geom. 19 (2021), no. 6, 1281–1337 - Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds (with Colin Guillarmou and Charles Hadfield)
Ann. Henri Poincaré 22 (2021), 3565–3617 - Pollicott-Ruelle resonant states and Betti numbers (with Tobias Weich)
Commun. Math. Phys. 378 (2020), 917–941 - Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces (with Tobias Weich)
Int. Math. Res. Not. 2021 (2019), no. 11, 8225–8296 - On the semiclassical functional calculus for h-dependent functions
Ann. Glob. Anal. Geom. 52 (2017), no. 1, 57–97 - Quantum ergodicity and symmetry reduction (with Pablo Ramacher)
J. Funct. Anal. 273 (2017), no. 1, 41-124 - Discontinuity of the Fuglede-Kadison determinant on a group von Neumann algebra
Commun. Math. 22 (2014), no. 2, 141-149
Until 2021 I published under my former surname Küster.
Edited works
- Mini-Workshop: (Anosov)^3 (with Colin Guillarmou, Beatrice Pozzetti and Tobias Weich)
Oberwolfach Rep. 18 (2021), no. 4, 3067-3099
Theses
- Symmetries in Hyperbolic Dynamics. Habilitation thesis, Universität Paderborn, 2024 (official version available after defense in mid 2025)
- Semiclassical Analysis of Schrödinger Operators on Closed Manifolds and Symmetry Reduction. PhD thesis, Phillips-Universität Marburg, 2015