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


Contact

 

Department of Mathematics

Ny Munkegade 118

building 1530, 423

8000 Aarhus C

Denmark

spilioti@math.au.dk

Phone: +4587155734


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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.