Title: Space vectors forming rational angles
We classify all possible configurations of vectors in three-dimensional space with the property that any two of the vectors form an angle whose measure is a rational multiple of π. As a corollary, we find all tetrahedra whose six dihedral angles are all rational multiples of π.While these questions (and their answers) are of an elementary nature, their resolution will take us on a tour through cyclotomic number fields, computational algebraic geometry, and an amazing fact about the geometry of tetrahedra discovered by two physicists in the 1960s. Joint work with Sasha Kolpakov, Bjorn Poonen, and Michael Rubinstein.
Dr Kedlaya is Professor of Mathematics and the Stefan E. Warschawski Chair in Mathematics at the University of California, San Diego.