The n/d conjecture for nonresonant hyperplane arrangements

Time：Wed., 16:00–17:00 Feb. 26, 2025

Venue：C654, Shuangqing Complex Building A

Organizer：Xiang He, Chenglong Yu, Dingxin Zhang, Jie Zhou

Speaker：Baiting Xie

Moduli Spaces and Related Topics

Organizers：

Xiang He, Chenglong Yu, Dingxin Zhang, Jie Zhou

Speaker：

Baiting Xie (Qiuzhen College, Tsinghua University)

Time：

Wed., 16:00–17:00

Feb. 26, 2025

Venue：

C654, Shuangqing Complex Building A

Title：

The n/d conjecture for nonresonant hyperplane arrangements

Abstract：

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 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 Chenglong Yu.

DATEFebruary 25, 2025

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