Normal functions and the Hodge conjecture

The Hodge conjecture has its origins in the work of Lefschetz
regarding which 2 dimensional homology classes on an algebraic surface
could be represented via algebraic curves on the surface. Lefschetz's
solution involved the study of a class of Poincare normal functions on
the Riemann sphere minus a finite number of points. In this talk, I will
outline Lefschetz's proof and discuss some recent work of Griffiths and
Green towards studying the Hodge conjecture for higher codimension
cycles using normal functions on higher dimensional parameter spaces.