LGRT 1322
The period-index problem is a longstanding problem in the theory of Brauer groups, which asks how the size of a division algebra is constrained by its order in the Brauer group. I will discuss a solution to the problem for Brauer groups of abelian threefolds, based on methods from derived categories, Hodge theory, and enumerative geometry. I will also describe the analogue of the problem for complex tori. Based in part on joint work with Alex Perry.