Ομιλήτρια : Πολυξένη Σπηλιώτη ( https://www.polyxenispilioti.com )
Ημερομηνία, ώρα : Παρασκευή 07 φεβρουαρίου 2025, 13:00
Τοποθεσία : Αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε ‘, 2ος όροφος.
Τίτλος : “The twisted Ruelle zeta function and the Ray-Singer metric”.
Περίληψη : “In this talk, we will present the twisted dynamical zeta functions of Ruelle and Selberg, associated with non-unitary, arbitrary representations of the fundamental group of an odd-dimensional compact hyperbolic manifold. D. Fried conjectured a relation, under certain assumptions, between the Ruelle zeta function at zero and a spectral invariant, the analytic torsion. This is widely known as the Fried’s conjecture and such a relation relates a pure geometrical-dynamical object, the Ruelle zeta function, with a spectral and a topological invariant. We will present some results concerning this conjecture as well as some recent results concerning the relation between the twisted Ruelle zeta function and the Ray-Singer metric of the refined analytic torsion associated with the representation, as it is introduced by Braverman and Kappeler “.