I am a researcher in the Heisenberg Programme of the DFG (German Research Foundation), currently based at Paderborn University in the Spectral analysis group. I am also an investigator in the Project Spectral theory in higher rank and infinite volume of the CRC TRR Integral Structures in Geometry and Representation Theory.
Recently I have been working a lot with locally homogeneous manifolds associated to discrete subgroups of Lie groups such as Anosov subgroups. I am especially interested in the geometry, the dynamical systems and the spectral theory on such manifolds, which often possess interesting pseudo-Riemannian structures. In another independent line of research, I study oscillatory integrals in symplectic geometry.
Photo by Petra Lein, from the Oberwolfach Workshop Anosov³ which I co-organized in 2021
News
- May 6, 2026: The paper A Riemann-Roch formula for singular reductions by circle actions joint with Louis Ioos and Pablo Ramacher has been accepted for publication in J. Inst. Math. Jussieu. In this paper we prove an equivariant Riemann-Roch formula for Hamiltonian circle actions on symplectic manifolds allowing fixed points, so that the symplectic reduction is an honest stratified space rather than a manifold or an orbifold. The formula involves a novel type of Kirwan-homomorphism which we call the exceptional Kirwan map.
- April 7, 2026: The paper Spectra of Lorentzian quasi-Fuchsian manifolds joint with Colin Guillarmou and Daniel Monclair has been accepted for publication in Commun. Math. Phys. In this paper we define a complete extension of the incomplete space-like geodesic flow for an interesting class of Lorentzian manifolds corresponding to a particularly instructive family of Anosov representations — the Lorentzian quasi-Fuchsian groups as studied in Barbot’s classical works. We furthermore develop a notion of quantum and classical resonances by meromorphic extension of resolvents. Remarkably, the classical situation of Ruelle resonances turns out to be simpler in this case than the quantum situation, i.e., the spectral theory of the pseudo-Riemannian Laplacian.
- April 2, 2026: I have been accepted into the Heisenberg Programme of the DFG (German Research Foundation). Project title: Smooth dynamics and resonance spectra in higher Teichmüller Theory. Press release at the Paderborn department: German, English
- April 1, 2026: I return to Paderborn University from my one-term leave to Leipzig University
- February 5, 2026: New version of the paper Patterson-Sullivan and Wigner distributions of convex-cocompact hyperbolic surfaces with Guendalina Palmirotta.
- October 23, 2025: Start of the joint Leipzig-Paderborn study group Variations on Character Varieties, which I am co-organising with Jacques Audibert from the MPI Leipzig and Guendalina Palmirotta and Tobias Weich from Paderborn University.
- October 1, 2025: I take up my position as Interim Professor for Geometry and Topology at Leipzig University, going on leave from Paderborn University. At the same time I became a visiting researcher at the Max Planck Institute for Mathematics in the Sciences
- September 1-5, 2025: I organise the conference Lie theory, Spectra and Dynamics at Paderborn University together with Guendalina Palmirotta and Tobias Weich.