Polyxeni Spilioti

 

I am a postdoctoral researcher at the Department of Mathematics, of the School of Applied Mathematical and Physical Sciences (SAMPS) of the National Technical University of Athens (NTUA).

Before, I held postdoctoral positions at the University of Göttingen in the group of Thomas Schick, at

Aarhus University  in the group of Jan Frahm, at the University of Tuebingen in the group of Anton Deitmar  and visiting postdoctoral positions at  Max Planck Institute for Mathematics and at the  Institut des Hautes Études Scientifiques. I received my PhD from the University of Bonn, under the supervision of Werner Mueller.

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Research interests:  Harmonic analysis on locally symmetric spaces, trace formulas, dynamical zeta functions of Ruelle and Selberg, refined analytic torsion, prime geodesic theorem

Contact: Office 329, Building E, Division of Applied Mathematics School of Applied Mathematical & Physical Sciences Polytechnioupolis Zographou, 157 80 Athens, Greece.

E-mail: xespil@mail.ntua.gr


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.