Department Colloquium
Department of Mathematics
Princeton University
March 29th, 2000
Geometric zeta functions on locally symmetric manifolds
Geodesics on a closed Riemann surface of constant negative curvature were assembled into a zeta function by Selberg. Subsequently, global properties of the surfaces were found to be expressible as "special values" of these zeta functions. I shall survey developments towards the constructions on locally symmetric manifolds of such geometric zeta functions. Various uses of harmonic analysis to compute topological invariants appearing in these functions will be highlighted. Examples of global geometric properties that can be extracted from these geometric zeta functions will be given.