Given a polynomial f, its Bernstein-Sato b-function b_f(s) is an important invariant with applications in analytic continuation of zeta-functions, birational geometry and D-modules. It is usually difficult to determine the roots of 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 U. Walther and use this result to prove the n/d-conjecture for weighted hyperplane arrangements satisfying the nonresonant condition. This is joint work with Baiting Xie.

About the Speaker: The speaker is now an assistant professor at Tsinghua University. His interests include geometry and arithmetic properties related to Calabi—Yau varieties, especially those moduli with Hermitian symmetric space structures. He also works on geometric and combinatorial invariants of hyperplane arrangements.