2000–2001 Erdős Colloquium:
Hyman Bass
The zeta function of a graph
Speaker: Hyman Bass, University of Michigan
Date and time: Friday, February 16, 2001, 4:00–5:00 p.m.
Location: Little Hall, Room 101
Introductory remarks: Neil Sullivan, Interim Dean of the College of Liberal Arts and Sciences
Cookies and coffee: 3:30 p.m., Little Hall, Room 339 (the Atrium)
Abstract
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.