Polyxeni Spilioti


I am a postdoctoral researcher at Aarhus University in the group of Jan Frahm.  Before I was a postdoctoral researcher in the group of Anton Deitmar at the University of Tuebingen. I received my PhD from the University of Bonn, under the supervision of Werner Mueller.

Research interests

  • Harmonic analysis on locally symmetric spaces
  • Trace formulas
  • Dynamical zeta functions of Ruelle and Selberg
  • Refined analytic torsion
  • Prime geodesic theorem

The field of spectral 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 powerful machinery in studying various invariants, such as the analytic torsion, as well as the dynamical zeta functions of Ruelle and Selberg.