Complex Algebraic Geometry

The method of multiplier ideals is one of the most versatile tools to study singularities of varieties. For the local theory, we present a connection between multiplier ideals and D-modules based on joint work with M. Mustata and M. Saito which has applications to Hodge spectra and Bernstein-Sato polynomials. For the global theory, we show how the space of unitary local systems on the complement of a divisor in a projective variety is a natural setting for studying global invariants of the singularities of the divisor involving multiplier ideals.