The zero locus of admissible normal functions -- Patrick Brosnan, April 2, 2010

Normal functions are sections of families of complex tori which arise when one considers families of homologically trivial algebraic cycles. For example, if X -> S is family of smooth curves and D is a relative divisor of degree 0, then one obtains a bundle of Jacobians, the Jacobians of the fibers, and D induces a section of this bundle. In general, normal functions are analytic objects. However, I will describe joint work with G. Pearlstein which shows that the zero locus of an admissible normal function is algebraic. This work can also be thought of as a generalization of the theorem of Cattani, Deligne and Kaplan. The main results have also been obtained by C. Schnell by a different method.