Abstract:

Abstract: I describe recent work with Greg Pearlstein proving that the zero locus of an admissible normal function is algebraic. I will explain why this is a generalization of a result of Cattani, Deligne and Kaplan showing that the Noether-Lefschetz locus is algebraic. I will also explain why the key step in the proof is a boundedness theorem for period maps. In addition, I will spend some time motivating the result and explaining how normal functions arose in Lefschetz's proof the Hodge conjecture for surfaces (the 1-1 theorem) and how they also are related to the Hodge conjecture for arbitrary varieities.