I am a postdoctoral researcher at the University of Tübingen, Department of Mathematics.

- Harmonic analysis on locally symmetric spaces
- Trace formulas
- Dynamical zeta functions of Ruelle and Selberg
- Refined analytic torsion

The field of sepctral geometry concerns with the connections between the geometry of manifolds and the spectrum of differential operators. The spectrum of the Laplace operator plays a crucial role in the inverse spectral problems. The most famous question relative to these problems was posed by Marc Kac in mid-60's :

* " Can one hear the shape of a drum ?
"*

The answer is not always positive, in particular when we deal with manifolds with singularities. This question can be alternatively expressed as:

*"How can one obtain information about the geometry of a manifold, such as the
volume, **the curvature, or the length of the closed geodesics, provided that we
can*

*study the spectrum of certain differential operators? "*

Harmonic analysis on locally symmetric spaces provides a poweful machinery in studying various invariants, such as the analytic torsion, as well as the dynamical zeta functions of Ruelle and Selberg.