Speaker: 邓太旺教授，BIMSA

Inviter: 聂思安研究员

Title: Orbital integrals of GLn over non-archimedean fields

Language: Chinese

Time & Venue: 2025. 04. 24 14: 30-16: 00 N818

Abstract: In 2014 Zhiwei Yun introduces a local L-factor whose special value at s = 0 computes the local orbital integral of type A. These L factors are controlled by the geometry of affine Springer fibers. In this talk, we will explain a conjectural construction of an affine paving for the affine Springer fibers based on the classical cell decomposition for compactified Jacobian by Piontkowski and show how to deduce Yun’s local L-factor from it. In the generic case this is known by work of Gorsky, Mazin and Oblomkov in 2024. In this case, I will explain my ongoing work with Su Tao attaching Young diagrams to the affine cells hence giving new proof of results obtaining by the three authors. As application, we apply our results to deduce a conjecture by Cherednik claiming that these local L-factors satisfy the Weil conjecture.