Seminars & Colloquia Calendar
Orthogonality of closed geodesics on the modular surface
Nigel Pitt (Maine)
Location: Hill 423
Date & time: Tuesday, 12 March 2019 at 2:00PM - 3:00PM
Abstract: Motivated by results from spectral theory that involve intersections and common perpendiculars between closed geodesics on the modular surface, we discuss how orthogonality of these closed geodesics relates to the classical theory of binary quadratic forms. The tools used are primarily from elementary number theory, but also from work by geometers and topologists from the 1990s (and earlier). We will also discuss how these methods allow us to consider "orthogonality" of positive definite forms, and how some of the results extend to 3-manifolds arising from Bianchi groups.
This is a work in progress.