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