报告题目：Bernstein-Sato polynomials for hyperplane arrangements

报告时间：2025-03-10  16:00-17:00

报 告 人：余成龙  助理教授（清华大学）

报告地点：雷军科技楼六楼会议室（644）

Abstract：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.