University of Sydney Algebra Seminar

John Voight

Friday 7 August, 12-1pm, in Carslaw 275

An orthogonal perspective on Gauss composition

Classical Gauss composition relates primitive binary quadratic forms of fixed discriminant to ideal or narrow ideal classes in the corresponding quadratic order.  We revisit Gauss composition over a general base, exhibiting a composition law which includes a universal version of Dirichlet composition, with a focus on orthogonal groups.  This synthesizes work of Kneser and Wood, reconciles algebraic and geometric approaches, and clarifies the emergence of narrow class groups.  This is joint work with Haochen Wu.