3-31【谢柏庭】The n/d conjecture for nonresonant hyperplane arrangements

Given a polynomial f, it is difficult to determine the roots of its b-function b_f explicitly. In particular, when f is a homogeneous polynomial of degree d with n variables, it is open to know when -n/d is a root of b_f. For essential indecomposable hyperplane arrangements, this is a conjecture by Budur, Musta\c{t}\u{a} and Teitler and implies the strong monodromy conjecture for arrangements. In this talk, I will introduce a cohomological sufficient condition given by  Walther and use this result to prove the n/d conjecture for weighted hyperplane arrangements satisfying the nonresonant condition. This is joint work with Chenglong Yu.