Third Gordon lecture

Speaker: Peter Sarnak (Princeton and IAS)

Title: Prescribing the spectra of cubic graphs

Abstract:

The bass note spectrum in this case is the study of cubic Ramanujan graphs. We examine what other gaps can be prescribed in their spectra and especially how these rigidfy as planarity further constraints such as fullerene structures are imposed. Among the tools used in this study are specific quantitative converses to Fekete's theorem about the distribution of galois conjugates of algebraic integers.