Mircea Mustata

In characteristic zero one associates to an ideal and a real exponent a multiplier ideal via an embedded resolution of singularities. The exponents for which the values of these ideals jump are called the jumping exponents. They provide fundamental invariants of the singularities of the subscheme defined by the ideal. In positive characteristic Hara, Takagi and Yoshida introduced an analogue of the multiplier ideals using the theory of tight closure. In particular, we get an analogue of the jumping numbers in positive characteristic. I will talk about joint work with Manuel Blickle and Karen Smith studying these invariants.