Appears in collection : 2025 - T1 - WS3 - Analysis on homogeneous spaces and operator algebras

In this talk, we present an analogue of the Atiyah-Singer Lefschetz fixed point theorem for generalized Hecke operators acting on a locally symmetric space of finite volume. We will discuss how the invariant trace formula can be applied to the difference of two heat kernels associated with Dirac operators on locally symmetric spaces. Additionally, we will explore applications, including an extension of the Osborne-Warner multiplicity formula to discrete series representations.