Title: Cohomology of Abelian Varieties

Abstract: Abelian varieties are compact complex tori that admit a holomorphic embedding into projective space.  As complex tori, their cohomology groups are elementary to describe.  On the other hand, describing the cohomology classes that arise from algebraic sub-varieties is much more difficult.  In this talk I will focus on so-called minimal cohomology classes in principally polarized abelian varieties.  The aim will be to introduce complex tori, discuss the example of Jacobians, and outline some past work on the problem, including some joint work with M. Popa and S. Schreieder.