-adic cycles
Periodic integrals and tautological systems
We study period integrals of CY hypersurfaces in a partial flag variety. We construct a regular holonomic system of differential equations which govern the period integrals. By means of representation theory, a set of generators of the system can be described explicitly. The results are also generalized to CY complete intersections. The construction of these new systems of differential equations has lead us to the notion of a tautological system.
Periods of Mixed Cusp Forms.
Picard-Lefschetz theory and characters of a semisimple Lie group.
Picard-Lefschetz theory for the coadjoint quotient of a semisimple Lie algebra.
Polarized Mixed Hodge Structures and the Local Monodromy of a Variation of Hodge Structure.
Problèmes de modules pour les formes différentielles singulières dans le plan complexe.