Around 1970, torsion points on elliptic curves were studied by using the
relation between topological and algebraic structures of their moduli
spaces, spaces which parametrize elliptic curves together with torsion
points. In this project, we replace elliptic curves with K3 surfaces,
which can be considered higher-dimensional analogues of elliptic curves.
The torsion points are replaced by the torsion part of the Brauer group
of the K3 surface, a group which plays an important role in the study of
rational points. This is joint work in progress with A. Várilly-Alvarado
and D. Bragg.
