Title: The Bernstein-Sato polynomial and the Strong Monodromy Conjecture
Speaker: Asilata Bapat (University of Chicago)
Abstract: To a singularity of an algebraic hypersurface, one can associate an invariant called the Bernstein-Sato polynomial or the b-function. Although the b-function is important and interesting, it is usually difficult to compute. It is conjectured (Strong Monodromy Conjecture or SMC) that some roots of the b-function can be obtained from the poles of another singularity invariant, the topological zeta function.
I will sketch the proof of the SMC for the case of Weyl hyperplane arrangements, via the "n/d conjecture" of Budur, Mustaţă, and Teitler. I will also describe some results towards computing the b-function of these arrangements, focusing on a special case (the Vandermonde determinant). This is joint work with Robin Walters.
Seminar URL: https://research.math.osu.edu/agseminar/
