Laboratoire Alexander Grothendieck, Institut des Hautes Études Scientifiques,
Morningside Center of Mathematics, Chinese Academy of Sciences,
Département des Sciences Mathématiques de l'Université de Tokyo

Ahmed Abbes (CNRS, IHÉS), Yongquan Hu (Morningside Center for Mathematics),
Fabrice Orgogozo (CNRS, École polytechnique), Takeshi Saito (Université de Tokyo),
Atsushi Shiho (Université de Tokyo), Ye Tian (Morningside Center for Mathematics),
Takeshi Tsuji (Université de Tokyo), Weizhe Zheng (Morningside Center for Mathematics)

Mercredi 10 avril 2019 de 10h30 à 11h30

Zongbin Chen (Yau Mathematical Sciences Center, Tsinghua University)

The geometry of the affine Springer fibers and Arthur's weighted orbital integrals

The affine Springer fibers are geometric objects conceived for the study of orbital integrals. They have complicated geometric structures. We will explain our work on the geometry of affine Springer fibers, with emphasize on the construction of a fundamental domain, and show how the study of the affine Springer fibers can be reduced to that of its fundamental domain. As an application, we will explain how to calculate Arthur's weighted orbital integrals via counting points on the fundamental domain.