Polyxeni Spilioti


Postdoctoral researcher

University of Tübingen

Raum 5 A29
Auf der Morgenstelle 10
72076 Tübingen

Germany

polyxenispilioti@gmail.com  


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

I completed my PhD studies at the Mathematical Institute of the University of Bonn under the supervision of Werner Mueller and held a visiting postdoc position at the Max Planck Institute for Mathematics in Bonn. I was an Oberwolfach Leibniz Fellow at the MFO, Oberwolfach Research Institute for Mathematics. I recently visited the Institut des Hautes Etudes Scientifiques (IHES).


Research interests

  • Global Analysis and Spectral Geometry
  • Harmonic analysis on locally symmetric spaces
  • Trace formulas
  • Dynamical zeta functions of Ruelle and Selberg
  • Refined analytic torsion


My research interests belong to the mathematical area of Spectral Geometry. As the name declares, this field concerns the connections between the geometry of manifolds and the spectum of differential operators.

The spectrum of the Laplace operator plays a crucial role for 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 is a poweful machinery in studying various geometric invariants, such as the analytic torsion, as well as the dynamical zeta functions of Ruelle and Selberg and spectral invariants.

 

It has numerous applications in mathematical physics, dynamics and ergodic theory.