Bass Note Spectra of Binary Forms

Explore a one-hour lecture from the Princeton University/Institute for Advanced Study Number Theory seminar where Giorgos Kotsovolis delves into the fascinating world of bass note spectra of binary forms. Learn about Mahler's 1940s program for determining bass note spectrum and its significance in the geometry of numbers and homogeneous dynamics. Discover how binary quadratic forms relate to the Markoff spectrum, and understand Mordell's work on binary cubic forms including his disproven conjecture about spectral gaps. Examine groundbreaking findings that demonstrate how the spectrum Spec(P) forms an interval for all binary forms of degree n≥3, contradicting earlier conjectures and advancing our understanding of this fundamental concept in number theory.