Computational Algebra Seminar
The eigenvalues of Hecke operators give rise to arithmetically interesting data. This talk will begin with a brief overview of one approach to computing Hecke operators on classical modular forms, but phrased in terms of Voronoi polyhedra and sharblies. I will describe some of the complications that arise when the change is made from the rational numbers to a number field. Then I will specialize to imaginary quadratic fields, giving a brief demonstration in Magma.
The Leech lattice is a remarkable object with many applications in group theory, number theory, coding theory and elsewhere. It lives in 24-dimensional space, and its many constructions are all rather technical. I outline a new approach which uses octonions to avoid many of the difficulties.