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

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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.