Polyxeni Spilioti

I am a postdocotral researcher in mathematics at the University of Patras in the group of D. Xatzakos. Before, I held postdoctoral positions at the National Technical University of Athens, University of Göttingen (group of T. Schick), Aarhus University (group of J. Frahm), and University of Tübingen (group of A. Deitmar).

I obtained my PhD from the University of Bonn under the direction of W. Müller.

Here is my

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Research interests: harmonic analysis on locally symmetric spaces, representation theory , Selberg and Ruelle zeta functions, Fried's conjecture, analytic torsion, prime geodesic theorem, pesudo-Riemannian spaces.

Contact: Department of Mathematics, School of Natural Sciences, University of Patras.

e-mail: pspilioti@upatras.gr

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Institut Henri Poincaré (IHP), Paris, France.

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 the powerful machinery for studying the connection between a spectral invariant, the analytic torsion, and the dynamical zeta functions of Ruelle and Selberg.