UF Mathematics
Erdos Colloquium

Spectral geometry relates the geometry of a Riemannian manifold to the spectrum of its Laplacian. A dramatic case of this is furnished by the Selberg zeta function of a Riemann surface, a kind of generating function for prime closed geodesics, whose zeros are related to the spectrum of its Laplacian. The talk will present a combinatorial analogue of this for finite graphs in place of Riemann surfaces. This was first introduced, in the case of regular graphs, by Ihara. The talk will be elementary and essentially self-contained.