Mixed Hodge Structures and Singularities

• 1. Gauss–Manin connection; 2. Limit mixed Hodge structure on the vanishing cohomology of an isolated hypersurface singularity; 3. The period map of a m-constant deformation of an isolated hypersurface singularity associated to Brieskorn lattices and mixed Hodge structures.

'Without any doubt, the author has covered a wealth of material on a highly advanced topic in complex geometry, and in this regard he has provided a great service to the mathematical community … he has succeeded in providing a brilliant introduction to, and a comprehensive overview of, this contemporary central subject of complex geometry … the entire text represents an irresistible invitation to the subject, and may be seen as a dependable pathfinder with regard to the vast existing original literature in the field.' W. Kleinert, Zentralblatt für Mathematik und ihre Grenzgebiete