Polyxeni Spilioti



 

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


Research interests

  • 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.