About Mircea Mustata's Work
My work is in algebraic geometry. I have been studying invariants that measure the singularities of algebraic varieties, such as minimal log discrepancies, log canonical thresholds, multiplier ideals, Bernstein-Sato polynomials, and F-thresholds. Various points of view and techniques come in the picture when studying these invariants: resolutions of singularities, jet schemes, D-modules, and positive characteristic methods. Most recently, I have been involved in a joint project with Mihnea Popa, studying some invariants of singularities, the Hodge ideals, that come out of the theory of mixed Hodge modules due to Morihiko Saito. One attaches to a given hypersurface in a smooth variety a sequence of ideals, the first of these being, the multiplier ideal, an object that has found many important applications in birational geometry.