Determinants of twisted Laplacians and the twisted Selberg zeta function

Date/heure
19 mars 2026
14:15 - 15:15

Lieu
Salle de séminaires Metz

Oratrice ou orateur
Polyxeni Spilioti (Univ of Patras)

Catégorie d'évènement
Séminaire Théorie de Lie, Géométrie et Analyse


Résumé

Let $X$ be a compact hyperbolic surface with finite order singularities and $X_1$ its unit tangent bundle. We consider the twisted Selberg zeta function $Z(s; \rho)$ associated with a representation $\rho: \pi_1(X_1) → GL(V_\rho)$. In this talk, we will present recent results concerning a relation between the twisted Selberg zeta function $Z(s; \rho)$ and the regularized determinant of the twisted Laplacian. The main tool we use is the Selberg trace formula.  If $X$ has no finite order singularities, we obtain as a corollary a corresponding relation. These results can be viewed as an extension to the non-unitary twists case of the results by Sarnak and Naud. This is joint work with Jay Jorgenson and Lejla Smajlovic.