Bernstein–Sato polynomials in positive characteristic

Kangaroo Points and Oblique Polynomials in Resolution of Positive Characteristic

In September 2008, Heisuke Hironaka gave a series of lectures at the Clay Mathematics Institute explaining his program for the resolution of singularities in positive characteristic [Hi1]. In the course of the lectures, Hironaka relied on results of the author from an unpublished manuscript written in 2003 [Ha1]. The quoted results investigate the main obstruction for resolution in positive cha...

Exceptional polynomials and monodromy groups in positive characteristic

Contents 1. Introduction 1

Characteristic Polynomials

Introduction. Let F be a field and let V be a finite dimensional vector space over F which is also a module over the ring F[a]. Here a may lie in any extension ring of F. We do not assume, as yet, that V is a faithful module, so that a need not be a linear transformation on V. It is known that by means of a decomposition of V into cyclic F[a]-modules we may obtain a definition of the characteri...

Oscillation Properties of Generalized Characteristic Polynomials for Totally Positive and Positive Definite Matrices

Expected Characteristic Polynomials

These notes are not necessarily an accurate representation of what happened in class. The notes written before class say what I think I should say. I sometimes edit the notes after class to make them way what I wish I had said. There may be small mistakes, so I recommend that you check any mathematically precise statement before using it in your own work. These notes were last revised on Decemb...