Given a holomorphic function f in n variables, its Bernstein-Sato polynomial is a classical invariant that detects the singularities of the zero locus of f in very subtle ways; for example, its roots recover the log-canonical threshold of f and the eigenvalues of the monodromy action on the cohomology of the Milnor fibre.
In my thesis I continue the work of Bitoun and Mustață to develop an analogue of this invariant in positive characteristic. More concretely, I develop a notion of Bernstein-Sato polynomial for arbitrary ideals (which, over the complex numbers, was done by Budur, Mustață and Saito), I show that its roots are always rational and negative and that they encode some information about the F-jumping numbers. I also prove that for monomial ideals one can recover the roots of the classical Bernstein-Sato polynomial from this characteristic-p version.

Eamon's advisor is Karen Smith.

Zoom: https://umich.zoom.us/j/94087016623
Password: bfunction Speaker(s): Eamon Quinlan (UM)