Ruijie Yang : p-adic integration of hyperplane arrangements and Hodge theory

Posted by Eamon Quinlan-Gallego , part of the Algebraic Geometry Seminar.

At

March 16, 2026, 3 p.m.

In

636 SEO

Abstract

Given a polynomial, the Strong Monodromy Conjecture predicts a mysterious relationship between its p-adic zeta function and Bernstein-Sato polynomial. While the conjecture remains widely open in general, progress has been made for specific classes of polynomials. In 2009, Budur-Mustațǎ-Teitler introduced the n/d conjecture and showed that it would imply the Strong Monodromy Conjecture for all hyperplane arrangements. In this talk, I will present a solution of the n/d conjecture, based on our new theory of multivariate V-filtration and a wall crossing theory for mixed Hodge modules. The latter is inspired by the recent breakthrough on the unitary dual problem of real Lie groups, by Davis-Vilonen. The talk is based on the upcoming work, joint with Dougal Davis.