Séminaire de Géométrie

# Dynamical zeta functions, trace formulae and applications

## by Mr Polyxeni Spilioti (Université de Tübingen)

Europe/Paris
E1180 (Bât E2) (Tours)

### E1180 (Bât E2)

#### Tours

Description

The dynamical zeta functions of Ruelle and Selberg are functions of a complex variable $$s$$ and are associated with the geodesic flow on the unit sphere bundle of a compact hyperbolic manifold. Their representation  by Euler-type products traces back  to the Riemann zeta function. In this talk, we will present  trace formulae and Lefschetz formulae, and the machinery that they provide to study the analytic properties of the dynamical zeta functions and their relation to spectral invariants. In addition, we will present other applications of the Lefschetz formula, such as the prime geodesic theorem for locally symmetric spaces of higher rank.