Robert Friedman
<br>
Title: Semi-algebraic horizontal subvarieties of Calabi-Yau
type
<br>
Abstract: I will discuss some joint work with R. Laza. We study
horizontal subvarieties of a
Griffiths period domain which are defined by algebraic
equations, i.e. which extend to a closed
subvariety of the compact dual of the period domain (which is a
projective variety). If the
horizontal variety is also invariant under a large discrete
subgroup in an appropriate sense,
then it is a Hermitian symmetric domain equivariantly embedded
in the period domain. We are
especially interested in the case where the Hodge structure is
of Calabi--Yau type. In this
case, the relevant variations of Hodge structure are
essentially those found by  Gross and
Sheng--Zuo, up to taking factors of symmetric powers and --
     --certain shift operations. The weight
three case can be quite explicitly described, and is related to
the study of homogeneous
Legendrian varieties.