Algebraic Geometry Seminar
Ruijie Yang
University of Kansas
p-adic integration of hyperplane arrangements and Hodge theory
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.
Monday March 16, 2026 at 3:00 PM in 636 SEO