Forschung

Ich forsche zu Themen der Differential- und metrischen Geometrie, der geometrischen und stochastischen Analysis, sowie zur harmonischen Analysis auf Lie-Gruppen.

Veröffentlichte Arbeiten und Preprints:

• Lower bounds on the normal injectivity radius of hypersurfaces and bounded geometries on manifolds with boundary. With Batu Güneysu and Stefano Pigola. 2025.
• A Chern-Simons transgression formula for supersymmetric path integrals on spin manifolds. With Sergio Luigi Cacciatori and Batu Güneysu. J. Geom. Phys., vol. 195, 2024.
• Feynman-Kac formula for perturbations of order ≤1 and noncommutative geometry. With Batu Güneysu. Stoch PDE: Anal Comp (2023) 11:1519–1552. 
• Relatively compact sets of Heisenberg manifolds. Differential Geometry and its Applications, Vol. 76 (2021).
• Scattering Theory and Spectral Stability under a Ricci Flow for Dirac Operators. With Batu Güneysu.To appear in Ann. Fac. Sci. Toulouse, Math. (6).Preprint
• Properties of the Dirac spectrum on three dimensional lens spaces. Osaka J. Math. 54, No. 4, 747-765
• An explicit formula for the Dirac multiplicities on Lens spaces. With E. A. Lauret. J. Geom. Anal. 27, No. 1, 689-725 (2017).

Buch (-kapitel):

• Contributions to the spectral geometry of locally homogeneous spaces. With Dorothee Schüth.Book chapter in Space - Time - Matter. Analytic and Geometric Structures. Brüning, J. (Ed.), Staudacher, M. (Ed.), Fiedler, B., et al. (2018). Berlin, Boston: De Gruyter. http://dx.doi.org/10.1515/9783110452150

Dissertation:

• The Height of compact nonsingular Heisenberg-like Nilmanifolds. Dissertation, Berlin, 2017.

Vorträge:

• The normal injectivity radius of a hypersurface. ULB geometry seminar. Université libre de Bruxelles. 2/2025.

• A Chern-Simons transgression formula for supersymmetric path integrals on spin manifolds. Oberwolfach Mini-Workshop "Recent Results on Loop spaces", 3/2025.

• The normal injectivity radius of an embedded hypersurface. Seminar "Functional analysis, operator theory and dynamical systems". Universität Leipzig. 7/2024

• Geometric scattering theory for Dirac operators. Conference: Recent results on analysis and geometry of (families of) Dirichlet spaces. 10/2023