The Hodge locus

I will report on a joint work with Klingler and Ullmo. Given a polarizable variation of Hodge structure on a smooth quasi projective variety S (e.g. the one associated to a family of pure motives over S), Cattani, Deligne and Kaplan proved that its Hodge locus (the locus of closed points of S where exceptional Hodge tensors appear) is a *countable* union of closed algebraic subvarieties of S. In this talk I will discuss when this Hodge locus is actually algebraic.

Proofs, applications and related results will be discussed in the forthcoming days.