Mathematics

The classical period map constructed by Griffiths is a map from the base of a family of smooth projective varieties to a subquotient of a Grassmannian, which associates to each point the Hodge filtration on cohomology of the fiber. This is an important
construction that can linearize moduli problems.
Manetti and others have studied a derived version of the infinitesimal period map on tangent complexes.
Jointly with Carmelo Di Natale I am working to extend these constructions to a global derived period map, studying a family of smooth projective varieties over a derived scheme. This is work in progress and the presentation will be informal.